Every developer has seen this:
0.1 + 0.2
// 0.30000000000000004
It's the most-shared bug in programming. You learn it, you nod, you move on — because in most code the error is so far down the decimal that nothing notices. A pixel is off by a billionth. A timer fires a nanosecond late. Nobody files a ticket.
Then you build a system whose entire job is to add thousands of numbers together and produce a total that has to match a figure someone calculated by hand. And the rounding error you waved away in the tutorial becomes a line in an audit report that says: the system total does not reconcile to the source data.
That's where I met this bug for real, building the calculation layer at GreenCalculus.com. It runs over a thousand emissions calculators, and every one of them has the same hard requirement: the number the engine produces must reconcile, to the last reported digit, against the number a practitioner gets when they check the math themselves. "Close enough" is a finding. This post is the set of rules that get you from the math looks right to the math reconciles.
Why this bites harder in measurement code than anywhere else
Most software treats numbers as means to an end — coordinates, counters, ratios feeding a render. The exact value rarely is the deliverable.
In emissions accounting, the number is the deliverable. A reported figure of 1,240.37 tCO2e is the product. If an auditor recomputes it and gets 1,240.41, the 0.04 isn't noise — it's an unexplained discrepancy, and unexplained discrepancies are exactly what an audit exists to surface. You don't get to say "floating-point." You get to fix your data model.
Three properties of this domain turn a harmless rounding error into a real defect:
- Massive summation. A Scope 3 inventory adds tens of thousands of line items. Error accumulates with count.
- Wide dynamic range. You add a 4,000,000 kg figure to a 0.002 kg figure in the same total. This is precisely the case floating-point handles worst.
- External reconciliation. The output is checked against an independent calculation. There's no hiding internal drift, because someone outside your system recomputes it.
The float problem, stated precisely
A 64-bit IEEE 754 float (double, JavaScript's only number type) stores 52 bits of mantissa — about 15–17 significant decimal digits. 0.1, 0.2, and 0.3 are not representable exactly in binary, the same way 1/3 isn't representable exactly in decimal. They're stored as the nearest available binary fraction, and the tiny errors survive arithmetic.
(0.1 + 0.2).toFixed(20)
// "0.30000000000000004441"
For a single operation the error is ~10⁻¹⁷. The problem is what happens when you do the operation 50,000 times, and when the operands differ in magnitude by a factor of a billion.
Failure mode 1: the total that won't reconcile
Naive summation of a long list of factors:
function totalEmissions(lineItems) {
let total = 0;
for (const item of lineItems) {
total += item.activity * item.factor; // each term carries float error
}
return total;
}
Each activity * item.factor lands on the nearest representable double, slightly off. Each += rounds again. Over tens of thousands of items the errors are mostly random and partly cancel — but "mostly" is not "exactly," and the residual is deterministic for a given input order. Run the same data through a spreadsheet that sums in a different order and you get a different last digit. Now you have two "correct" totals that disagree, and no way to say which is right.
Fix: control precision at the boundary, not in the loop
Two defensible strategies, depending on stack.
Decimal arithmetic for the money-and-mass path. Store and sum factors as arbitrary-precision decimals so there's no binary-representation error at all:
import Decimal from 'decimal.js';
function totalEmissions(lineItems) {
return lineItems
.reduce((acc, item) =>
acc.plus(new Decimal(item.activity).times(item.factor)),
new Decimal(0))
.toNumber(); // convert once, at the very end, after rounding regime applied
}
Decimal is slower. You don't need it everywhere — you need it on the path whose output is a reported figure.
Kahan summation when you must stay in floats. If the hot path can't afford Decimal, compensated summation recovers most of the lost low-order bits by tracking the rounding error and feeding it back in:
function kahanSum(values) {
let sum = 0;
let compensation = 0; // running error term
for (const v of values) {
const y = v - compensation;
const t = sum + y;
compensation = (t - sum) - y; // recovers what the addition just dropped
sum = t;
}
return sum;
}
The single addition sum + y loses the low bits of y when sum is large; the next line reconstructs exactly those bits and carries them into the following iteration. For a long sum of mixed-magnitude terms this is the difference between a stable total and one that drifts with input order.
Failure mode 2: the wide-magnitude swallow
This is the one that produces a wrong number, not just an unstable one.
let total = 4_000_000.0; // a large facility's annual figure, kg
total += 0.002; // a trace fugitive line, kg
total === 4_000_000.002; // true here — but stack enough trace lines...
When the accumulator is large and the addend is tiny, the addend's significant bits fall off the bottom of the mantissa and are silently dropped. One trace line is fine. Ten thousand of them, each individually swallowed, is a missing category total. The sum looks authoritative — it's a clean large number — which is exactly why nobody catches it by eye.
Fix: sum within magnitude bands, then combine
Add small things to small things before adding them to big things. Sort ascending and the smallest terms accumulate among themselves into a magnitude the large accumulator can actually absorb:
function bandedSum(values) {
const ascending = [...values].sort((a, b) => a - b);
return kahanSum(ascending); // small-first ordering + compensation
}
Sorting ascending before a compensated sum is a cheap, robust default for "many small, few large." It won't matter on uniform data — but reference-data sums are rarely uniform.
Failure mode 3: the ratio that amplifies
Intensity metrics divide one computed figure by another — emissions per unit revenue, per tonne of product, per kWh. Division doesn't create error, but it amplifies whatever error the operands already carry, and ratios of two nearly-equal slightly-wrong numbers are the worst case.
const intensityA = total2025 / output2025;
const intensityB = total2024 / output2024;
const yoyChange = (intensityA - intensityB) / intensityB; // tiny - tiny, over tiny
When intensityA and intensityB are close, their difference is dominated by the rounding error in each, and dividing that noisy difference by a small base inflates it into a visible percentage. Your year-on-year intensity change can read as ±0.3% pure artefact.
Fix: defer rounding, widen the working precision
Carry full precision through the entire chain and round once, at presentation. Never round an intermediate that feeds a later division. If the figures are reconciliation-critical, do the division in Decimal too — the cost is trivial relative to one division per report.
Failure mode 4: the unit-boundary shave
Every conversion is a multiply, and every multiply is a place to lose digits. The g → kg → t chain looks innocent:
const grams = 1234567;
const kg = grams / 1000; // 1234.567
const tonnes = kg / 1000; // 1.234567
// round-trip back up and compare:
tonnes * 1000 * 1000 === grams; // not guaranteed
Each division lands on the nearest double; chaining them compounds the drift, and a value that round-trips through three units may not come back to where it started. The fix is the same architectural rule that governs the whole post: store in one canonical unit at full precision, convert only at the display boundary. Don't persist the converted value and re-derive from it — persist the canonical value and convert on read.
The rule underneath all four
Every one of these is the same decision made wrong: where does precision get fixed, and how many times. The failures all come from rounding early, rounding repeatedly, or rounding in the middle of a chain that isn't done yet.
The architecture that prevents all four:
- One canonical unit, full precision, in storage. No pre-rounded, pre-converted values persisted.
- A declared rounding regime, applied once, at the boundary. Half-up, half-even — pick one, document it, apply it where the number leaves the system, never before.
- Decimal on any path whose output is a reported figure. Floats are fine for charts and progress bars. They are not fine for the deliverable.
- Compensated, magnitude-aware summation wherever you must aggregate many terms in floating point.
This is the same shape as a rule we apply to every figure in the GreenCalculus data layer: a number is meaningless without its declared basis. There, the basis is the GWP version and the emission-factor source. Here, it's the unit and the rounding regime. In both cases the discipline is identical — the number is not just its digits; it's its digits plus the declared rules that produced them. Store the rules with the number, or you can't defend the number.
0.1 + 0.2 was never the bug. It was the warning that your numbers carry rules you haven't written down yet.
The GreenCalculus calculation layer applies these rules across 1,000+ emissions calculators, every one of which has to reconcile against its source data to the last reported digit. Methodology documentation at greencalculus.com.
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