A round steel bar's mass in kilograms per metre is its diameter in millimetres, squared, divided by 162, and by our arithmetic that shortcut reads 0.121% heavy at every bar size. Hong Kong's CS2:2012 builds its mass table on steel weighing 0.00785 kg per square millimetre of cross-section per metre. Multiply that by the area, πd²/4, and the divisor comes out at 4 ÷ (π × 0.00785), or 162.196. On a bar schedule the bias is 1.2 kg per tonne. The same standard lets a test specimen of bar over 8 mm deviate by up to ±4.5% from its nominal mass per metre, about 37 times the shortcut's error.
A rounded constant takes the blame for the shortcut's extra weight
The shortcut is the exact formula with its divisor rounded down, and a smaller divisor gives a bigger answer, so d²/162 reads high by the same proportion at every size. None of that is new. Most write-ups of the shortcut that rank in search derive 162.2 from steel's density of 7,850 kg/m³. What we could not find was the error laid out size by size against a standard's own table and set beside the tolerance a bar is tested to. Many ranking charts follow India's IS 1786; ours is Hong Kong's table, so a third decimal may differ from theirs.
An open Hong Kong table faults the shortcut in the third decimal
The Civil Engineering and Development Department's Construction Standard CS2:2012 covers bars from 6 to 50 mm and in its foreword refers to BS 4449:2005+A2:2009. Its Table 2 gives each size a nominal mass: the kilograms per metre run of a bar of exactly the nominal diameter.
For a 12 mm bar, d²/162 gives 0.889 kg/m and Table 2 prints 0.888. Against the table the shortcut runs from 0.02% over at 8 mm to 0.13% over at the larger sizes, and it is over at every one. Rounded to three decimals, it disagrees with the table at seven of the ten sizes, all from 12 mm up.
The exact formula does not reproduce the table either. Rounded, it gives 1.578 kg/m for 16 mm where Table 2 prints 1.579, and it misses by one in the third decimal at 25 and 40 mm too. We could find no single rounding recipe behind the table, and the table, rather than any formula, is what the standard publishes.
Mass tolerance on a test specimen forgives the formula 37 times over
CS2's Table 3, set out for grades 250, 500B and 500C, gives the permissible deviation from nominal mass per metre run: ±4.5% for bars over 8 mm and ±6.0% for bars of 8 mm and under. Clause 6.2 applies it to a test specimen.
Beside those figures the shortcut's 0.121% is about a 37th of the larger-bar allowance and a 50th of the smaller, on our arithmetic. One is a fixed bias in a formula, the other an allowance for a single specimen in a testing regime. Whether a bar passes is settled by testing under its product standard, and these allowances are Hong Kong's.
Two-decimal shortcuts punish the smallest bars
By our arithmetic, a chart that rounds d²/162 to two decimals does more damage than the rounded constant. For 8 mm it prints 0.40 kg/m, 1.27% above the table's 0.395. At 6 mm the error flips sign: 0.22 against 0.222, which is 0.90% light. A 10 mm bar comes out at 0.62, 0.49% heavy. From 16 mm up the two-decimal figure stays within 0.16% of the table, because a hundredth of a kilogram is a small share of a heavier bar.
Bar-count conventions, more than the formula, set a schedule's spread
Mass per metre is half of a take-off, the quantity estimate for a job; the other half is length, which depends on how bars are counted. With the first bar on one edge, floor(span ÷ spacing) + 1 places bars only at whole multiples of the spacing; where the span is not a whole multiple, the last bar stops short of the far edge by a strip narrower than one spacing. Adding a bar on that edge gives one more each way.
On 14 October 2026 we ran both counts over 901 square slabs from 1.00 to 10.00 m, in 1 cm steps, at 200 mm spacing. In 855 the span was not a whole multiple of the spacing. Averaged over all 901, the far-edge count added 4.67% to total bar length. The difference narrows as slabs grow, from 16.7% on a 1.1 m slab to 2.0% on a 9.9 m one. A 5.1 m slab gains 3.85%, and even the smallest figure is many times the formula's 0.121%. We found no primary source that settles which count a take-off should use.
Until 14 October 2026 our rebar weight calculator used the whole-spaces count only, which its method note disclosed. The revision made that day offers "Whole spaces only", selected by default, and "Add a far-edge bar", and each result names the count it used and gives the other's figure: 47 bars against 49 on a 5.1 by 4.1 m slab at 200 mm. It also corrected its 12 mm example to 0.889 and limited its eighths-of-an-inch rule to #8. Its result is a mass estimate for one mesh layer and makes no claim to be a reinforcement design.
US bar numbers overlook the inch fraction above #8
In US practice a bar's number is its nominal diameter in eighths of an inch only up to #8. Caltrans's Bridge Design Details, Table 13.1.1, its September 2025 table of ASTM bar data for A706 Grade 60, lists a #14 bar at 1.693 in. Fourteen eighths would be 1.75 in, 3.37% wider.
Applied to each diameter in that table, d²/162 lands between 0.09% and 0.31% above Caltrans's listed weight per foot, by our arithmetic.
Every jurisdiction's standard answers for its own mass table
Hong Kong's CS2:2012 is the easy case, a free PDF naming the BS 4449 edition it refers to. We did not open BS 4449 itself, which BSI sells.
Singapore's standard for these bars, SS 560:2016(2024)+A1:2024, is listed as current on the Singapore Standards eShop, confirmed with amendments in 2024, with six grades from B500A to B600C. The listing does not mention BS 4449. Its mass table and tolerances sit behind the purchase; we have not seen them. Amendment 1 of August 2024, which is free, changes the references, chemical composition and traceability clauses and leaves dimensions and mass alone.
Malaysia's is MS 146:2014, whose text the Department of Standards Malaysia sells. We read a CIDB presentation by Ir. Sabrudin Suren of CIDB's iron and steel expert panel, dated 16 December 2015. It says the standard "is identical to BS 4449:2005" and, under clause 7.4.2, gives a mass tolerance of ±6.5% for bars of 8 mm and under and ±4.5% above. That ±6.5% does not match CS2's ±6.0%, though both point back to BS 4449:2005, and without the standard's own text we could not tell which is right.
For rebar mass, only Hong Kong's table could be read in full and free of charge on 14 October 2026. The Singapore and Malaysian tables are their standards bodies' to publish.
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