Rebar Weight: Where d²/162 Comes From

The formula is just a cylinder

A reinforcement bar is a steel cylinder, so its mass per metre is its cross-sectional area times the density of steel. Area is π/4 × d², and every standard that matters here — IS 1786, BS 4449, ASTM A615 — agrees the density is 7850 kg/m³.

That is the entire derivation. There is nothing else in it. Rearranged so you can put the diameter in as millimetres instead of metres, it collapses to a single division:

kg/m = d² ÷ 162.196

A 16 mm bar is 256 ÷ 162.196 = 1.5783 kg/m. A 20 mm bar is 400 ÷ 162.196 = 2.4662 kg/m. You can check any row of any chart in about ten seconds, which is worth doing once, because charts do disagree.

The divisor is 162.196, not 162

The number everyone carries is 162, and it is a fine thing to carry — it is easy to remember and you can do it in your head on site.

But it is rounded down. The exact value is 4 000 000 ÷ (π × 7850) = 162.196, and using 162 instead makes every mass read 0.121% high. On a tonne of steel that is about 1.2 kg.

That is far inside any wastage allowance, so this is not a reason to stop using the shortcut. It is the reason two charts sometimes disagree in the last digit, and knowing which one you are looking at stops you chasing a discrepancy that was never an error.

The number that actually costs money

Weight is the easy half. The half that goes wrong is the bar count.

Almost every schedule works it out as total length divided by stock length, rounded up. That quietly assumes every offcut finds another cut to serve. On a real site it usually does not.

Three 7 m cuts is 21 m of steel, so the arithmetic says two 12 m bars. But no two 7 m cuts fit on one 12 m bar, so you need three — and 15 m of the 36 m you bought is scrap. The estimate was not slightly optimistic; it was a whole bar short.

It is not always wrong. Three 5 m cuts genuinely is two bars, because 5 + 5 fits with a metre to spare. That is exactly why the shortcut survives: it is right often enough that nobody stops trusting it.

Working a schedule properly

Take each bar mark: diameter, cut length, number of bars. Put laps, hooks and bend allowances into the cut length itself rather than adding a percentage at the end — those allowances differ by standard and by detail, and a flat percentage hides which one you used.

Multiply cut length by count by mass per metre for the weight of each mark. Total by diameter, because that is the unit steel is ordered in: nobody buys the slab's steel, they buy so many tonnes of 12 and so many of 16.

Then work out the bars separately by packing the cuts, and compare that count to the division. The gap between them is steel you will buy and not use.