DEV Community: Keith So

The Math Behind Early Retirement (FIRE) And What Most Calculators Get Wrong

Keith So — Mon, 09 Mar 2026 08:01:33 +0000

You've probably seen the FIRE pitch: save aggressively, invest, retire at 40. The subreddits are packed with spreadsheets and projections. But most back-of-napkin FIRE math makes the same mistakes, and they compound badly over a 20-year horizon.

Let's break down the actual math, where the popular shortcuts fail, and how to run the numbers properly.

The Core FIRE Equation

FIRE boils down to one question: how many years until my investment portfolio covers my annual spending?

The classic rule of thumb is the 4% rule (from the 1998 Trinity Study). If your annual expenses are X, you need 25X saved. That's it. Simple division.

FIRE number = Annual expenses / 0.04

Spending 30,000/year? You need 750,000.

But this formula hides three assumptions that quietly wreck projections.

Mistake #1: Ignoring Inflation During Accumulation

The 4% rule accounts for inflation-adjusted withdrawals in retirement, but most people forget inflation during the savings phase.

If you earn 60K and spend 30K today, you're saving 30K/year. But in 15 years at 3% inflation, that same lifestyle costs 46,739. Your FIRE number just jumped from 750K to 1.17M.

Future expenses = Current expenses x (1 + inflation)^years
Adjusted FIRE number = Future expenses / withdrawal_rate

This alone adds 3-7 years to most projections. Try it with real numbers

Mistake #2: Using Average Returns Instead of Sequence of Returns

Markets don't return a steady 7% per year. They crash, they spike, they go sideways.

A portfolio averaging 7% over 30 years might look like:

Scenario	Year 1-5 avg	Year 6-30 avg	Final value (500K start)
Steady	7%	7%	3.81M
Early crash	-8%	9.4%	2.94M
Late crash	9.4%	5.2%	3.12M

Same average. Different outcomes. The early crash scenario is the killer during retirement because you're selling low to fund expenses.

This is called sequence of returns risk, and it's why a single number like "7% growth" is dangerously misleading.

Mistake #3: Treating the Withdrawal Rate as Fixed

The 4% rule assumes a 30-year retirement. If you're retiring at 35, you need that money to last 50-60 years. The safe withdrawal rate drops.

Research from Wade Pfau and others suggests:

Retirement length	Safe withdrawal rate
30 years	4.0%
40 years	3.5%
50 years	3.25%
60 years	3.0%

At a 3% withdrawal rate, your FIRE number for 30K/year spending isn't 750K. It's 1,000,000. That's a 33% increase from a single variable change.

Putting It All Together

A proper FIRE calculation needs:

Current savings and monthly contribution
Expected return (use real returns, net of inflation, around 4-5% historically)
Current annual expenses inflated to your target retirement date
Withdrawal rate adjusted for your expected retirement length
Tax treatment of withdrawals (ISA vs pension vs general account matters hugely in the UK)

The formula for years to FIRE, accounting for compound growth on contributions:

Years = ln((FIRE_number * r + C) / (P * r + C)) / ln(1 + r)

Where:
  P = current portfolio value
  C = annual contribution
  r = real annual return (after inflation)
  FIRE_number = annual expenses / withdrawal rate

This is a log equation, which means the relationship between savings rate and years to retirement is non-linear. Going from a 30% savings rate to 50% doesn't cut your timeline by a third. It might cut it in half.

The Savings Rate Curve

Here's what the numbers look like at a 5% real return, starting from zero:

Savings rate	Years to FIRE (4% rule)	Years to FIRE (3% rule)
20%	37 years	42 years
30%	28 years	33 years
40%	22 years	26 years
50%	17 years	21 years
60%	12 years	16 years
70%	9 years	12 years

The jump from 50% to 70% savings rate saves you 8-9 years. The math heavily rewards higher savings rates.

Run Your Own Numbers

I built a FIRE calculator that handles all of this: inflation-adjusted expenses, variable withdrawal rates, and compound growth on ongoing contributions. No signup, runs in your browser.

If you want to explore the components separately:

Compound interest calculator to model portfolio growth scenarios
Inflation calculator to see what your expenses will actually be in 20 years
Savings goal calculator to reverse-engineer monthly contributions

The Honest Take

FIRE math isn't hard. It's logarithms and compound growth. The hard part is the inputs: predicting returns, inflation, tax policy, and your own spending over decades.

Anyone who gives you a single number without showing sensitivity analysis is selling you a fantasy. Run the numbers yourself, stress-test the assumptions, and plan for the version where things don't go perfectly.

The spreadsheet doesn't care about your feelings. That's what makes it useful.

3 UK Money Checks I Run Before Saying Yes to a Pay Rise

Keith So — Mon, 02 Mar 2026 08:01:35 +0000

3 UK Money Checks I Run Before Saying Yes to a Pay Rise

Most salary conversations focus on one number: gross pay.

But when your pay crosses certain UK thresholds, your effective gain can be much smaller than expected.

I keep a simple checklist and run the same three calculations every time I get an offer, raise, or contract change.

1) Check for the GBP 100k tax trap first

In the UK, your Personal Allowance is reduced by GBP 1 for every GBP 2 earned above GBP 100,000.

That means in the GBP 100k-GBP 125,140 range, many people face an effective 60% marginal rate (before National Insurance and student loan effects).

So if your salary goes from GBP 99,000 to GBP 109,000, the headline increase can feel great, but the take-home uplift can be underwhelming.

Use this first:

UK 100k Tax Trap Calculator

Quick sanity check

If a raise puts you just into that band, options like pension salary sacrifice can sometimes improve outcomes more than a straight cash increase.

2) Model student loan repayments on the new salary

Many people estimate repayments with rough percentages and get it wrong.

For Plan 2 borrowers, repayments are based on income above the threshold, so higher salary usually increases monthly deductions immediately.

Before accepting a raise, I test both scenarios:

current salary
proposed salary

Then compare annual repayment difference:

UK Student Loan Calculator

This prevents the classic "I got a raise but my payslip barely moved" surprise.

3) Convert the raise into real (inflation-adjusted) terms

A 5% raise in a 4% inflation environment is not a 5% improvement in buying power.

Run a quick real-value check:

Inflation Calculator

If your nominal pay is up but real pay is flat, that changes how you evaluate the offer - and how hard you negotiate non-cash benefits.

A practical decision framework

When I compare two offers (or old vs new salary), I track four values:

Gross salary difference
Net annual take-home difference after tax + loan effects
Pension impact (especially if salary sacrifice is available)
Real-terms gain after inflation

Only then do I decide whether the raise is genuinely meaningful.

Why this matters

Most people don't need more financial theory - they need a faster way to avoid bad assumptions.

That's why I built these calculators: quick, no-signup checks you can run in 2 minutes before making a decision.

No signup. No email capture. Just math.

Salary Sacrifice: The Tax Hack Every UK Developer Should Know

Keith So — Sun, 01 Mar 2026 10:50:00 +0000

Most UK developers leave thousands of pounds on the table every year because nobody explains salary sacrifice properly. Not your employer, not your accountant, definitely not HMRC.

Here's how it actually works, with real numbers at real salary levels.

What salary sacrifice actually is

You agree with your employer to reduce your gross salary. The amount you give up goes straight into your workplace pension. Because it never hits your pay slip as income, you don't pay income tax or National Insurance on it.

That second part is the key. Personal pension contributions get income tax relief, but you still pay NI. Salary sacrifice dodges both.

The numbers at different salary levels

On 30,000 pounds (basic rate taxpayer)

Sacrifice 200 pounds per month into pension:

Income tax saved: 40 pounds (20%)
NI saved: 16 pounds (8%)
Cost to your take-home: 144 pounds
Amount going into pension: 200 pounds
Effective discount: 28%

On 50,000 pounds (higher rate taxpayer)

Sacrifice 500 pounds per month:

Income tax saved: 200 pounds (40%)
NI saved: 10 pounds (2% above UEL)
Cost to your take-home: 290 pounds
Amount going into pension: 500 pounds
Effective discount: 42%

At higher rate, you're getting 500 pounds into your pension for a 290 pound reduction in take-home. That's a 72% return on day one.

On 80,000 pounds (solid senior dev salary)

Sacrifice 800 pounds per month:

Income tax saved: 320 pounds (40%)
NI saved: 16 pounds (2%)
Cost to your take-home: 464 pounds
Amount going into pension: 800 pounds
Effective discount: 42%

On 120,000 pounds (in the 100k tax trap)

This is where it gets wild. Sacrifice 1,667 pounds per month (20,000 per year) to bring taxable income to 100,000 pounds:

Income tax saved: 667 pounds per month (40%)
Personal allowance restored: saves an additional 419 pounds per month
NI saved: 33 pounds per month
Cost to your take-home: 548 pounds
Amount going into pension: 1,667 pounds
Effective discount: 67%

You're putting 1,667 pounds into your pension every month and it only costs you 548 pounds in take-home pay. The rest was going to HMRC anyway.

Salary sacrifice vs personal pension contributions

	Salary Sacrifice	Personal Pension
Income tax relief	Yes (automatic)	Yes (20% added, claim rest via SA)
NI saving (employee)	Yes	No
NI saving (employer)	Yes (15%)	No
Reduces taxable income	Yes	Yes
Affects mortgage applications	Yes (lower gross)	No
Affects student loan	Yes (calculated on lower salary)	No

The mortgage point is the main trade-off. Lenders look at your gross salary, and salary sacrifice reduces it. If you're about to apply for a mortgage, time your sacrifice carefully.

The employer NI bonus

Here's something most people miss. When you sacrifice salary, your employer also saves 15% NI on that amount. Some employers pass this saving into your pension too.

On a 500 pound monthly sacrifice, your employer saves 75 pounds in NI. If they pass it on, you're getting 575 pounds into your pension for a 290 pound take-home reduction. Ask your HR team if they do this.

Student loan interaction

Salary sacrifice reduces your gross salary for student loan calculation purposes. If you're on Plan 2 (9% above 27,295 pounds) and sacrifice 300 pounds per month, that's 27 pounds less in student loan repayments each month. Not life-changing, but it adds up.

When salary sacrifice isn't worth it

Near national minimum wage: sacrifice can't take you below NMW. Your employer will block it.
Need the cash now: if you're saving for a house deposit and need every pound liquid, pension contributions (even tax-efficient ones) aren't helpful.
About to apply for a mortgage: as mentioned, lower gross salary means lower borrowing capacity.
Already maxing annual allowance: the pension annual allowance is 60,000 pounds (2025/26). If employer and employee contributions combined exceed this, you'll face a tax charge.

How to set it up

Ask your employer if they offer salary sacrifice for pension contributions (most medium-large companies do)
Decide how much to sacrifice (use a salary sacrifice calculator to see the exact take-home impact)
Fill in the paperwork (usually an amendment to your employment contract)
Check your next pay slip to confirm it's working

If your employer doesn't offer salary sacrifice, you can still make personal pension contributions and claim higher-rate relief through Self Assessment. You lose the NI saving, but you keep the income tax benefit.

The bottom line

If you're a higher rate taxpayer (above 50,270 pounds), salary sacrifice into pension is one of the most tax-efficient things you can do. The numbers aren't small: a senior developer earning 80,000 pounds who sacrifices 10,000 pounds per year saves roughly 4,200 pounds in tax and NI. That's real money.

If you're earning over 100,000 pounds and not using salary sacrifice, you're actively paying thousands more tax than you need to. Run your numbers through the 100k tax trap calculator to see exactly how much.

UK Tax Calculator | Pension Calculator | Salary Sacrifice Calculator

All figures based on 2025/26 England/Wales rates.

The UK Developer Tax Trap Nobody Warns You About

Keith So — Sun, 01 Mar 2026 10:49:21 +0000

You got the promotion. You're earning 105,000 pounds. You check your pay slip expecting a nice bump.

It's barely more than when you were on 99,000 pounds.

Welcome to the UK's 100k tax trap, the most punishing stretch of the entire tax system, and one that hits software developers disproportionately hard.

The maths that makes you angry

When your income crosses 100,000 pounds, HMRC claws back your 12,570 pound Personal Allowance at a rate of 1 pound for every 2 pounds you earn above the threshold. That income that was previously tax-free? Now taxed at 40%.

Here's what that actually means per pound earned between 100k and 125,140 pounds:

40p income tax (higher rate)
20p effective tax from losing your personal allowance (50% of 40%)
2p National Insurance

Total: 62p of every pound goes to HMRC.

That's a higher marginal rate than someone earning 500,000 pounds (who pays 47%).

A real example: 99k vs 110k

On 99,000 pounds, you keep your full 12,570 pound personal allowance. Take-home after tax and NI: roughly 64,500 pounds.

On 110,000 pounds, you've lost 5,000 pounds of personal allowance. Take-home: roughly 69,200 pounds.

An extra 11,000 pounds gross gives you only 4,700 pounds more in your pocket. The rest, about 6,300 pounds, went to HMRC. That's an effective rate of 57% on that chunk of income.

Why this matters for developers

The average UK software engineer salary is around 55k-65k. Senior engineers and tech leads in London regularly hit 80k-120k. Contractors inside IR35 can easily land in this zone.

If you're a senior dev negotiating a raise from 95k to 110k, you might assume that 15k bump means 9k more take-home. It doesn't. You'd see about 6,400 extra, because 10k of that raise falls in the trap zone.

The fix: salary sacrifice into pension

The most common escape is salary sacrifice. You redirect some of your salary into your workplace pension before tax is applied.

Example: you earn 115,000 pounds and sacrifice 15,000 pounds into pension.

Your taxable income drops to 100,000 pounds
Your full personal allowance (12,570 pounds) is restored
You save approximately 5,000 pounds in income tax you would have lost to the taper
You save 300 pounds in NI on the sacrificed amount
Your employer saves 15% NI on the sacrificed amount too (some employers pass this saving to you)

Net cost to you: roughly 9,700 pound reduction in take-home pay, but 15,000 pounds goes into your pension. That's a 54% return before any investment growth.

Should you care?

If you earn between 100,000 and 125,140 pounds: yes, absolutely. The numbers are too large to ignore.

If you're approaching 100k: plan now. Talk to your employer about salary sacrifice before your next pay rise pushes you into the zone.

If you're a contractor: this applies to your deemed salary if you're inside IR35, or your dividends and salary mix if you're running a Ltd company.

Run your own numbers

I built a free 100k tax trap calculator that shows your exact marginal rate and optimal salary sacrifice amount. There's also a salary sacrifice calculator if you want to model different contribution levels.

No signup, no email capture. Just the maths.

All figures based on 2025/26 England/Wales tax rates. Scotland has slightly different bands (42% higher rate) but the personal allowance taper works the same way.

The Math Behind Compound Interest (And Why It Breaks Your Intuition)

Keith So — Mon, 23 Feb 2026 08:06:44 +0000

Most people know compound interest is powerful. Few people know why it feels so unintuitive.

Here's the thing: human brains think linearly. We expect 100/year to become 1,000 in 10 years. Compound interest doesn't work that way, and the gap between what we expect and what actually happens is where the real money lives.

Let me break down the actual math.

The Formula (It's Simpler Than You Think)

ext A = P(1 + r/n)^(nt)

Where:

A = final amount
P = principal (starting amount)
r = annual interest rate (as decimal)
n = compounding frequency per year
t = time in years

That's it. One formula. But the magic is in the exponent nt. Exponents are what make this non-linear, and non-linear is what breaks your brain.

A Real Example

Say you invest 10,000 at 7% annually, compounded monthly, for 30 years.

Linear thinking says: 7% of 10,000 = 700/year x 30 = 21,000 in gains. Total: 31,000.

Actual result: 10,000 x (1 + 0.07/12)^(360) = 81,165

That's not a small rounding error. Linear thinking underestimates the real result by 61%.

Try it yourself with different numbers

Where the Money Actually Comes From

Here's the year-by-year breakdown that makes this click:

Period	Balance	Interest Earned That Year
Year 1	10,700	700
Year 5	14,026	918
Year 10	19,672	1,288
Year 20	38,697	2,534
Year 30	76,123	4,987

In year 1, you earn 700. In year 30, you earn 4,987 on the same original investment. The interest is earning interest, which earns more interest.

More than half your total gains come in the final 10 years. This is why starting early matters more than investing more.

The Frequency Question

Does compounding monthly vs. annually actually matter?

10,000 at 7% for 30 years:

Frequency	Final Amount	Difference vs. Annual
Annually	76,123	--
Quarterly	79,957	+3,834
Monthly	81,165	+5,042
Daily	81,662	+5,539

Monthly to daily? Nearly identical. But annual to monthly? That's a meaningful 5K difference on a 10K investment.

The Part Nobody Talks About: Inflation

Here's the uncomfortable truth that compound interest evangelists skip. Inflation compounds too, in the opposite direction.

If your investment grows at 7% but inflation runs at 3%, your real return is roughly 4%. That 81,165 nominal result? In today's purchasing power, it's closer to 33,400.

Still great. Still way better than a savings account. But the posts showing 10K becomes 80K are quietly ignoring that 80K won't buy what 80K buys today.

See how inflation erodes purchasing power with an inflation calculator.

What This Means Practically

1. Start now, not later.
Starting 10 years earlier with 5K beats starting later with 15K. The exponent does the work, but it needs time.

2. Regular contributions dominate.
10K one-off grows to 81K in 30 years. But adding just 200/month? That's 262,481. The monthly contributions matter more than the starting lump sum over long periods.

Use a savings goal calculator to figure out exactly how much you need to save monthly to hit a target.

3. Don't interrupt compounding.
Every time you withdraw and restart, you reset the exponent. A 30-year run beats three 10-year runs, even with the same rate, because the exponential curve is steepest at the end.

4. Real returns, not nominal.
Always think in real (inflation-adjusted) terms. A 7% return with 3% inflation is a 4% real return. Plan accordingly.

The Bottom Line

Compound interest isn't magic. It's an exponential function, and exponential functions are genuinely hard for human brains to estimate. Now you know the formula, the real numbers, and the inflation caveat that most explainers skip.

The best time to start was yesterday. The second best time is right now.

All calculators mentioned are free at boring-math.com. No sign-up, no tracking, instant results.

The Real Math Behind Going Freelance as a Developer

Keith So — Mon, 23 Feb 2026 08:04:24 +0000

Going freelance is one of those decisions that looks obvious on paper. You're billing 500/day instead of earning 60k/year. That's 130k if you work 260 days. Easy money, right?

Not even close.

I've watched developers make this leap without running the numbers properly, and the ones who struggle almost always made the same mistake: they compared their gross freelance rate to their net employee salary.

Here's the math they missed.

The Hidden Costs of Freelancing

When you're employed, your salary is the tip of the iceberg. Your employer is paying:

Employer National Insurance (13.8% on earnings above the threshold)
Pension contributions (minimum 3%, often 5-10%)
Holiday pay (28 days minimum, roughly 11% of working days)
Sick pay, parental leave, training budget
Equipment, software licenses, office space

A 60k employee typically costs the employer 72-80k. That's your real compensation package.

The Freelance Rate Equation

To match a 60k salary as a freelancer, you need to account for:

1. Billable Days Are Not Working Days

There are roughly 260 working days in a year. Subtract:

25-30 days holiday (you still want time off)
5-10 days sick or personal
20-40 days for admin, marketing, invoicing, chasing payments
10-20 days between contracts (bench time)

Realistic billable days: 180-200 per year

2. Tax and National Insurance (UK)

As a sole trader or limited company director, your tax structure changes completely:

Corporation tax (25% on profits over 50k via Ltd)
Self-assessment tax and NI (sole trader)
Dividend tax if extracting via Ltd
No employer NI subsidy
VAT registration (mandatory above 90k turnover)

3. Benefits You Now Pay For

Professional indemnity insurance: 300-600/year
Public liability insurance: 100-300/year
Pension contributions: you fund 100% now
Equipment and software: 1,000-3,000/year
Accountant: 1,000-2,500/year
Co-working space: 0-4,000/year

4. The Real Minimum Rate

Taking a 60k salary with typical benefits (pension, holiday, NI):

Total compensation value: roughly 75,000

Divide by 190 billable days: 395/day minimum

That's just to break even with your old job. To actually come out ahead and compensate for the risk and instability, most advisors suggest a 40-50% premium, putting you at 550-600/day.

The Contractor vs Employee Decision

The calculation gets more interesting when you factor in:

IR35 status (inside vs outside, massive tax difference)
Career progression (no promotions, but no ceiling either)
Mortgage applications (lenders want 2-3 years of accounts)
Compound effects (employer pension matching is free money you're walking away from)

I built a contractor vs employee calculator that handles the full comparison, including tax differences, pension, insurance, and bench time.

Setting Your Rate

Once you've decided to go freelance, pricing is the next trap. Most developers either:

Undercharge because they anchor to their salary
Overcharge and can't find work
Don't adjust for market, location, or specialization

The formula I recommend:

```n Target annual income (post-tax)

All business costs
Tax provision (set aside 25-30%)
Risk buffer (10-15%) = Required gross revenue

Required gross revenue / Billable days = Day rate




A [consulting rate calculator](https://boring-math.com/calculators/consulting-rate-calculator) makes this concrete. Plug in your target take-home, expenses, and tax situation, and it gives you the day rate you actually need.

For US readers, the W2-to-1099 conversion is similarly brutal. Self-employment tax alone is 15.3%, and you lose employer healthcare contributions. A [freelance rate calculator](https://boring-math.com/calculators/freelance-day-rate-calculator) that accounts for these differences is worth using before you hand in your notice.

## When It Makes Sense

Freelancing *does* make financial sense when:

- Your skills command a rate premium (specialist > generalist)
- You can maintain 80%+ utilization (strong network or niche demand)
- You're disciplined about saving for tax and retirement
- The flexibility has genuine lifestyle value to you

It doesn't make sense when:

- You're optimizing purely on gross numbers
- You haven't built a network yet
- You need mortgage approval in the next 2 years
- You undervalue employer benefits

## Run Your Own Numbers

Generic advice only goes so far. Your situation has specific variables: your tax bracket, your employer's pension match, your realistic utilization rate, your insurance costs.

Tools that helped me think through this:

- [Contractor vs Employee Calculator](https://boring-math.com/calculators/contractor-vs-employee-calculator) - side-by-side comparison with full tax treatment
- [Consulting Rate Calculator](https://boring-math.com/calculators/consulting-rate-calculator) - work backwards from your target income
- [Freelance Day Rate Calculator](https://boring-math.com/calculators/freelance-day-rate-calculator) - quick rate calculation with expense factoring

The math isn't complicated. But it is easy to get wrong if you skip the boring parts.

I Built 125 Free Calculators for Lifes Boring Math

Keith So — Wed, 18 Feb 2026 09:57:54 +0000

Have you ever tried to figure out how much alcohol to buy for a wedding? Or what your freelance day rate should be? Or whether its cheaper to buy or rent?

I kept running into these boring math problems - not hard, but tedious enough that Id open a spreadsheet, fumble with formulas, and waste 20 minutes on what should take 30 seconds.

So I built boring-math.com - 125 free calculators for the everyday math nobody wants to do by hand.

Whats in there

The calculators cover everything from personal finance to party planning:

Money stuff:

Compound interest calculator - see how your savings grow over time
Buy vs Rent calculator - the actual math behind the biggest financial decision most people make
Freelance day rate calculator - convert salary to day rate accounting for tax holidays and pension
Savings goal calculator - how much to save monthly to hit your target

Life stuff:

Wedding alcohol calculator - dont run out, dont overbuy
BBQ calculator - meat per person, sides, the works
Baby cost calculator - the real first year costs

Health and utility:

And about 110 more.

The tech

Built with Astro + Preact + Tailwind CSS. Static site deployed on Cloudflare Pages.

Each calculator is a single .astro page with an interactive Preact component for the actual calculation. No backend, no database, no accounts. Just math.

Why Astro? Perfect for content-heavy sites with islands of interactivity. The calculators need JavaScript but the surrounding content - explanations, FAQs, related links - is pure HTML. Astros island architecture means you only ship JS where you need it.

Performance: Lighthouse 90+ across all pages, local fonts, lazy-loaded interactive components.

What I learned building 125 of these

1. Every calculator needs context, not just inputs.

A compound interest calculator with just the math is boring. But add a worked example showing what happens if you start 5 years earlier? Now its useful content that Google actually wants to rank.

2. Related calculators create rabbit holes.

Someone using the savings goal calculator probably also wants the compound interest calculator. Internal linking between related tools keeps people on the site and helps SEO.

3. Schema markup matters.

Every calculator has WebApplication + FAQ + BreadcrumbList structured data. Tedious to set up but Google Search Console immediately started showing richer impressions.

4. The long tail is real.

Nobodys outranking the big sites for mortgage calculator. But additional dwelling supplement calculator Scotland? Those niches have real search volume and almost no competition.

Try it out

The whole thing is free, no sign-up required: boring-math.com

If youve got a calculator idea I havent built yet, drop it in the comments - always looking for the next piece of boring math to automate.