Section shapes, formulas and reference weights
10 shapes with the closed-form area formula each one uses. Area is what turns dimensions into weight, and it is the only part of the calculation that depends on the shape — density is a single number whatever the geometry.
All 10 shapes at one reference size
Every shape below is shown at the same nominal size — 25 mm, or 10 mm thickness for plate — in carbon steel at 7,850 kg/m³. Comparing across rows is the point: at equal nominal size a square bar is 27 % heavier than a round bar, and a hollow section is a fraction of either.
Plate’s mass is per metre of a 1,000 mm wide strip, which is numerically its mass per square metre — the unit plate is actually bought in.
Solid bars
Round, square and hexagonal stock. Sold by diameter or across-flats.
Round Bar
A = π/4 · d²
A = π/4 × d², where d is the outside diameter
Round bar is the only shape whose area grows with the square of a single dimension, so small diameter changes move weight much faster than intuition suggests: going from 25 mm to 28 mm — a 12 % diameter increase — raises the weight per metre by 25 %. This is why shaft stock is normally bought to the nearest preferred diameter rather than machined down from the next size up; the material saved is more than the weight table implies.
- Parameters
- d — Diameter
- Reference size
- d = 25 mm → 490.9 mm², 3.853 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified by diameter only. For ground and polished stock, add the tolerance class and the straightness limit.
Weight tables with this shape
Square Bar
A = a²
A = a², where a is the side length
A square bar has 27.3 % more area than the round bar that circumscribes it (a = d) and 21.5 % more mass — the corners of the square sit outside the circle. The reverse comparison is more useful in practice: a round bar of diameter d fits inside a square of side d with material to spare, so swapping square for round at the same nominal size removes about 21 % of the weight and produces a very similar-looking part.
- Parameters
- a — Side
- Reference size
- a = 25 mm → 625.0 mm², 4.906 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified by side. State whether corners must be sharp or radiused; standard stock usually has a small corner radius.
Weight tables with this shape
Hexagonal Bar
A = (√3/2) · AF² ≈ 0.8660 · AF²
A = (√3/2) × AF², where AF is the distance across flats (the wrench size), not across corners
Hex bar is the one shape where the ordering dimension is not the dimension the formula wants. Stock is sold by across-flats (AF) because that is what the wrench grips, but the area formula needs AF as well — and the two are easy to confuse once a drawing quotes across-corners instead. Across-corners is a factor of 2/√3 (1.1547) larger than AF, so mixing them up inflates the calculated weight by 33 %. Always check which one the drawing calls out.
- Parameters
- AF — Across flats (AF)
- Reference size
- AF = 24 mm → 498.8 mm², 3.916 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified by across-flats. Say so explicitly on the order — "across corners" gives a different bar.
Weight tables with this shape
Flat and plate
Rectangular sections up to plate width. Stocked in standard thicknesses.
Flat Bar
A = w · t
A = w × t, where w is width and t is thickness
Flat bar is where the site’s most common estimating mistake shows up: weight is independent of how the bar is oriented, but stiffness is not. A 50 × 6 flat bent about its strong axis is roughly 69 times stiffer than the same bar bent about its weak axis, while both weigh 2.36 kg/m. Reading weight off a flat-bar table tells you what to order; it tells you nothing about whether the section will carry the load.
- Parameters
- w — Width · t — Thickness
- Reference size
- w = 50 mm, t = 6 mm → 300.0 mm², 2.355 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified as width × thickness. Edge condition (square, radiused, or sheared) changes the effective area slightly, not the nominal weight.
Weight tables with this shape
Plate
A = w · t
A = w × t. For plate the useful output is mass per unit area: m″ = t × ρ
Plate is the one product where the customer usually wants mass per unit area rather than per unit length, because plate is priced and handled by the square metre. Reducing thickness by a fraction of a millimetre has an outsized commercial effect: stepping a 6 mm floor plate down to 5 mm removes 16.7 % of the steel on a job that may be measured in thousands of square metres. That is also exactly why plate thickness tolerances are specified separately from the nominal value — a permitted negative tolerance on a nominally 6 mm plate is real money at scale.
- Parameters
- w — Width · t — Thickness
- Reference size
- w = 1000 mm, t = 10 mm → 10,000.0 mm², 78.500 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified as thickness × width × length, plus the tolerance class and whether the pattern is plain, chequer or floor plate.
Weight tables with this shape
Hollow sections
Round, square and rectangular tube. The best stiffness per kilogram.
Round Tube
A = π/4 · (D² − d²), d = D − 2t
A = π/4 × (D² − d²), where D is the outside diameter, d the inside diameter, and d = D − 2t for wall thickness t
Hollow sections are the most efficient way to buy stiffness by weight, and the numbers are stark: a 50 mm outside diameter tube with a 3 mm wall has the same area as a 22.6 mm solid bar — about 20 % of the mass — but its second moment of area is roughly 2.4 times larger. The catch is local: a thin wall buckles and dents long before it yields, so tube is chosen for stiffness and stability, never for where impact or crushing is expected.
- Parameters
- D — Outside diameter · t — Wall thickness
- Reference size
- D = 50 mm, t = 3 mm → 443.0 mm², 3.477 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified as outside diameter × wall thickness. State the standard (e.g. EN 10219) and whether the tube is welded or seamless.
Weight tables with this shape
Square Tube
A = a² − (a − 2t)²
A = a² − (a − 2t)², which expands to A = 4t(a − t)
Square tube expands cleanly to A = 4t(a − t), which makes the sensitivity obvious: for a given side, weight is almost exactly linear in wall thickness. Doubling a 2 mm wall to 4 mm adds about 1.9 times the mass, not twice, because the inner void shrinks as the wall grows. Its flat faces also make it the natural choice for welded frames and for anything that has to be drilled, tapped or bolted through a face — a round tube gives you only a tangent point where a square tube gives you a full flat.
- Parameters
- a — Side · t — Wall thickness
- Reference size
- a = 40 mm, t = 3 mm → 444.0 mm², 3.485 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified as side × wall thickness. Corner radii are standardised per EN 10219 and change the area slightly at heavier walls.
Weight tables with this shape
Rectangular Tube
A = a·b − (a − 2t)(b − 2t)
A = a·b − (a − 2t)(b − 2t), which expands to A = 2t(a + b) − 4t²
Rectangular tube is the shape to reach for when a beam has to be shallower than it is wide in one direction only. Because depth drives bending stiffness far more than width does, taking a rectangular section and turning it 90° changes the stiffness dramatically while the weight stays identical — a 100 × 50 × 4 tube is about 4 times stiffer about its strong axis than its weak axis, at 9.10 kg/m either way. The table here holds the common 2:1 depth-to-width proportion; enter your own dimensions in the calculator when the section is not 2:1.
- Parameters
- a — Depth · b — Width · t — Wall thickness
- Reference size
- a = 60 mm, b = 40 mm, t = 3 mm → 564.0 mm², 4.427 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified as depth × width × wall thickness. Confirm which dimension is the depth on a drawing before computing loads.
Weight tables with this shape
Structural sections
Angles and channels. Multi-dimensional, sold by named size.
Angle (L Section)
A = t · (a + b − t)
A = t × (a + b − t), where a and b are the two leg lengths and t the thickness. Equal-leg angles set a = b, giving A = t(2a − t)
The angle formula quietly removes a double-counted corner: A = t(a + b − t) is t times each leg, less one t² for the square where the legs overlap. Skipping that correction overstates the area of a 50 × 50 × 5 angle by 10 %. Angles also bend about neither leg — the governing axis passes through the centroid, which sits off both legs, and it is why an equal angle is normally used back-to-back with a twin where bending matters. This table holds legs equal; put unequal legs into the calculator when the drawing specifies them.
- Parameters
- a — Leg a · b — Leg b · t — Thickness
- Reference size
- a = 50 mm, b = 50 mm, t = 5 mm → 475.0 mm², 3.729 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified as leg a × leg b × thickness. Say whether the toe is square or radiused, and whether it is equal-leg.
Weight tables with this shape
Channel (U Section)
A = 2·b·t_f + (h − 2·t_f)·t_w
A = 2 × b × t_f + (h − 2 × t_f) × t_w, where h is the overall depth, b the flange width, t_f the flange thickness and t_w the web thickness
Channel is the only shape here with four independent dimensions, and it is the one where a supplier’s actual product most often differs from the drawing: nominal channel sizes are named by depth while the flange width, web and flange thicknesses vary between standards and even between mills. The weight consequence is real — a 200 mm channel with a 7.5 mm web and a 200 mm channel with an 8.5 mm web differ by about 4 % in mass. For anything ordered by the tonne, get the mill’s section mass and use the calculator only for sanity checks.
- Parameters
- h — Depth · b — Flange width · t_w — Web thickness · t_f — Flange thickness
- Reference size
- h = 200 mm, b = 75 mm, t_w = 8 mm, t_f = 10 mm → 2,940.0 mm², 23.079 kg/m in carbon steel at 7,850 kg/m³
- When ordering
- Specified by depth in a named standard (UPN 200, C8×11.5, MC 200) — never by depth alone, because different standards use different webs and flanges.
Weight tables with this shape
Data source and method Every area on this page comes from the closed-form formula shown next to it — there is no tabulated area data anywhere on the site. Masses are computed as area × 10⁻⁶ × 7,850 for carbon steel.
- Elementary plane geometry. The circle, polygon and hollow-section area formulas.
- BIPM / NIST definitional constants: international inch = 25.4 mm, foot = 0.3048 m, pound = 0.45359237 kg.
Dataset version 2026.09.1 · dimensions last verified against source 2026-09-21. Found an error? Report it — corrections are issued with a version bump.