Two rebar weights that look 8% apart are actually 61% apart

A rebar takeoff landed on my desk that balanced to the last bar and was still wrong by two tonnes.

Every bar was the right length. Every count matched the drawing. The error was upstream of the arithmetic: two schedules had been converted from metric to imperial by someone who compared the numbers instead of the units.

This is the least glamorous failure mode in quantity takeoff, and it survives every review because the arithmetic downstream is perfect. Wrong inputs, clean math, confident total.

Here are the three conversions where it happens, how much each one costs, and the check that catches them.

Trap 1: the bar substitution that adds 61%

A slab schedule says 10 mm bars at 200 mm centres, both ways. A fabricator in a US market quotes #4 at 8 inches and calls it equivalent.

The supporting logic is usually something like this: 10 mm is about 3/8 inch, #4 is 1/2 inch, close enough. That is already two approximations deep, and the second one is not close at all.

The unit weights look deceptively similar, which is why nobody questions them:

• 10 mm metric bar: 0.617 kg/m
• #4 bar: 0.668 lb/ft

0.668 and 0.617 differ by 8%. That looks like rounding noise between two published tables. It is not. Different units, so the digits are not comparable:

0.668 lb/ft × 1.4882 kg/m per lb/ft = 0.994 kg/m

The real gap is 0.994 vs 0.617, which is 61% heavier per metre. Same nominal "one bar per 200 mm" grid, 61% more steel.

The area check says the same thing without any conversion table:

Bar	Nominal diameter	Area	Unit weight
10 mm metric	10.0 mm	78.5 mm²	0.617 kg/m
#3 (3/8")	9.5 mm	71 mm²	0.560 kg/m
#4 (1/2")	12.7 mm	129 mm²	0.994 kg/m

129 / 78.5 = 1.64. #4 carries 64% more area than 10 mm. It is not the soft-metric equivalent of a 10 mm bar; #3 is the nearest US size, and even that is 10% under on area.

Worked example: 500 m² of slab

Both directions at 200 mm centres gives 5 running metres per square metre per direction:

10 mm:  10 m/m² × 0.617 kg/m = 6.17 kg/m²  → 500 m² = 3,085 kg = 3.09 t
#4:     10 m/m² × 0.994 kg/m = 9.94 kg/m²  → 500 m² = 4,970 kg = 4.97 t

+1.88 t, +61%. If the spacing is converted honestly (8 in = 203.2 mm, so slightly fewer bars), it drops to +58%. Either way, the line item is over by more than half and the slab is over-reinforced against a design that was checked for 10 mm.

The reverse substitution is the one that gets people hurt: swapping #4 for 10 mm to "save steel" cuts the area by 39% on a section that was designed, checked and approved at 78.5 mm².

Trap 2: scaling a squared formula linearly

The standard metric unit weight is:

w = 0.00617 × d²        (kg/m, d in millimetres)

It comes straight out of density and area:

7850 kg/m³ × π/4 × (d/1000)² = 0.006165 d²

The exponent is the part people drop. Given a table entry for Φ10 at 0.617 kg/m, a Φ12 bar gets estimated as 0.617 × 12/10 = 0.740 kg/m. The correct value is 0.888 kg/m — the linear guess is 16.7% low.

Worked example: 1,200 bars of Φ12, 6.0 m each

Correct:  0.888 kg/m × 6.0 m × 1,200 = 6,394 kg = 6.39 t
Linear:   0.740 kg/m × 6.0 m × 1,200 = 5,328 kg = 5.33 t

Short by 1.07 t on a 6.4 t package. That is not a rounding difference at the invoice; it is a second delivery, usually on a minimum-order charge, usually on the day the pour is scheduled.

Two more variants of the same bug, both of which I have seen survive review:

• Diameter in centimetres. 0.00617 × 1.2² = 0.0089 kg/m. Off by a factor of 100. This one is almost always caught, because the tonnage collapses to something absurd.
• Diameter in inches. 0.00617 × 0.5² = 0.0015. Also caught, but only if someone sanity-checks against a known bar.

The squared term punishes interpolation too. Between Φ12 (0.888 kg/m) and Φ25 (3.856 kg/m), the midpoint of the weight column is 2.372. The actual Φ18 and Φ19 bars inside that gap weigh 2.00 and 2.23 kg/m. Averaging two neighbours overstates the middle of the range by roughly 12% — produced by the most reasonable-looking step in the whole process. If the diameter is missing from the table, square it; do not average the weights.

Trap 3: tonne, ton, and the 10% that hides in a word

Rebar is quoted per tonne in most of the world and per short ton in the US. One letter apart:

1 short ton  = 2,000 lb = 907.2 kg
1 metric tonne = 1,000 kg

A 40-unit package invoiced in short tons delivers 36.3 tonnes of actual steel. On a 40 t order, 3.7 t is missing — roughly one floor's slab of a small building — and every document says "40".

Concrete has the same shape of problem, in cubic yards:

1 yd³ = 0.7646 m³      1 m³ = 1.3079 yd³

14.4 m³ of slab is 18.83 yd³. Rounding the factor to 0.75 gives 19.2 yd³ — 2% over, which is inside normal waste allowance and therefore invisible. Rounding to 1.3 instead of 1.3079 goes the other way and under-orders by 0.6%.

The conversion table worth taping to the wall

Quantity	The number people reuse	What it actually is	Error if used as-is
#4 unit weight	0.668 (as kg/m)	0.994 kg/m	−33%
#3 unit weight	0.376 (as kg/m)	0.560 kg/m	−33%
1 lb/ft	1.5 kg/m	1.4882 kg/m	+0.8%
1 short ton	1,000 kg	907.2 kg	+10%
1 yd³	0.75 m³	0.7646 m³	−1.9%
1 in	25 mm	25.4 mm	−1.6%

Sort that column by magnitude and the priority is obvious. Two of these will blow a budget line. Three of them are noise you can ignore without losing sleep — and knowing which is which is most of the skill.

What actually catches these

Three habits, none of them clever:

Carry units in the cell, not in your head. 0.668 lb/ft and 0.617 kg/m are different objects. A schedule row that says only "0.668" invites the next reader to assume the unit they were already thinking about.

Cross-check every weight against area, not against another weight. A = πd²/4, then × 7850. If two numbers disagree, the area check tells you which one is wrong, because diameter is the one input you can measure with a caliper.

Sanity-check the total against steel per cubic metre. Ordinary reinforced concrete sits around 80–150 kg/m³. A slab that comes out at 40 or 260 is not a clever optimisation; it is a unit error.

I keep the arithmetic in a calculator rather than in a spreadsheet cell, mostly so the unit stays attached to the input: rebar weight calculator takes diameter, length, count and waste allowance, and returns kg/m, per-bar weight and total tonnage. There are sibling pages for lap length, bend deduction and stirrup cutting length built the same way — one input per row, unit stated, formula printed on the page so the result can be checked by hand.

None of this is difficult mathematics. It is bookkeeping, and bookkeeping fails quietly.

The takeoff that started this post was off by two tonnes because two numbers eight percent apart were assumed to be the same number. They were never the same quantity. A unit is not a label you drop when the arithmetic gets going — it is the thing that decides whether 0.668 means a bar weighs 33% less than it does.