The metal weight formula

The weight of any solid metal part comes from one idea: weight equals density times volume. For a constant cross-section — a bar, tube, plate or angle of fixed profile — the volume is just the cross-section area times the length. Put together, the metal weight formula is:

W = ρ · A · L

where:

• ρ — the material’s density (mass per unit volume).
• A — the cross-section area of the profile.
• L — the length of the piece.

Every metal-weight question reduces to getting these three numbers into consistent units. Pick the right density (see the material density chart), work out the area of your profile, multiply by length, and convert.

Cross-section areas

The only part that changes with shape is the area A. The common profiles:

• Round bar — A = π/4 · d² (d = diameter).
• Square bar — A = a² (a = side).
• Hexagon bar (across flats) — A = (√3/2) · AF² (AF = across-flats size).
• Flat / plate — A = w · t (width × thickness).
• Round tube — A = π/4 · (OD² − ID²) (subtract the bore).
• Rectangular tube — A = b · h − (b − 2t)(h − 2t) (outer area minus inner cavity).

A tube or hollow section is always the solid outer area minus the area of the hole, so the same W = ρ · A · L still applies — you just feed it a hollow area. For standard pipe sizes you can read the wall thickness straight off the steel pipe schedule chart rather than measuring.

The hexagon area is worth a closer look, because it is the one people misremember. For a regular hex measured across the flats (the AF size you read with callipers, and the dimension hex stock is sold by), the area is (√3/2) · AF² ≈ 0.866 · AF². If you only have the across-corners distance, that is the larger dimension and the area formula is different — so always confirm which one you measured.

Densities of common metals

Density is the multiplier that turns volume into weight, so using the right value matters more than any other input. Typical room-temperature densities:

Material	Density (g/cm³)
Steel (carbon / low-alloy)	7.85
Stainless steel	8.0
Cast iron	7.2
Aluminium	2.70
Brass	8.5
Copper	8.96
Titanium (Ti-6Al-4V)	4.43

Note how much spread there is: aluminium is roughly a third the weight of steel for the same shape, and titanium under 60% — which is exactly why those metals get used where weight is the constraint.

A unit-consistent formula you can actually compute

Densities are quoted in g/cm³, but profiles are measured in millimetres. Rather than converting everything to centimetres, fold the conversion into a single constant. If area is in mm² and length in mm:

W(kg) = density(g/cm³) × area(mm²) × length(mm) / 1,000,000

The factor of 1,000,000 converts mm³ to cm³ (1000) and grams to kilograms (1000). For stock sold by the metre, drop the length and you get weight per metre:

W(kg/m) = density(g/cm³) × area(mm²) / 1000

Worked example 1 — steel round bar

A Ø25 mm steel round bar, 1 m (1000 mm) long. First the area:

A = π/4 · 25² = 0.7854 × 625 ≈ 490.9 mm²

Then the weight, with steel at 7.85 g/cm³:

W = 7.85 × 490.9 × 1000 / 1,000,000 ≈ 3.85 kg

So a one-metre length of 25 mm steel bar weighs about 3.85 kg — and the weight-per-metre is the same 3.85 kg/m. (This is exactly what the calculator returns for these inputs.)

Worked example 2 — steel plate

A steel plate 1000 × 500 × 10 mm. Here the volume is direct: 1000 × 500 × 10 = 5,000,000 mm³ (= 5000 cm³). Multiply by density and divide by 1000 to get kilograms:

W = 5,000,000 mm³ × 7.85 g/cm³ / 1000 = 39.25 kg

The same plate in aluminium (2.70 g/cm³) would weigh 5000 × 2.70 / 1000 = 13.5 kg — a third as much, as the density table predicts.

Angles, channels and rolled shapes

The W = ρ · A · L recipe still holds for an equal- or unequal-leg angle, a channel or any other constant section — the only difficulty is the area. An angle, for example, is two legs that share one corner, so its area is A = t · (a + b − t) for legs a and b of thickness t (the − t avoids double-counting the overlapping corner). For rolled structural shapes with filleted roots and tapered flanges — I-beams, UB/UC sections — the published mass-per-metre in the section tables already bakes in those radii, so use the table value rather than a simplified area; a sharp-cornered approximation runs a few percent light.

A practical shortcut for repeat work is to compute weight per metre once for a given profile and material, then multiply by length as needed. That is the number steel suppliers quote, and it lets you price or load-check a cut list with a single multiplication.

Working in imperial units

The formula is identical; only the density units change. In imperial, density is in pounds per cubic inch (lb/in³), so weight is simply:

W(lb) = density(lb/in³) × volume(in³)

Steel is about 0.284 lb/in³, aluminium about 0.098 lb/in³ and copper about 0.323 lb/in³. Get the volume in cubic inches (area in in² times length in inches) and multiply — no extra conversion constant needed, because the density already carries the right units.

Whatever the shape or unit system, the recipe is the same: density × area × length, with the area formula chosen to match the profile. The calculator handles every profile above, the SI⇄imperial toggle and the per-length figure in one step.

Frequently asked questions

What is the formula for the weight of a metal bar?

Weight = density × volume, and volume = cross-section area × length, so W = ρ · A · L. In unit-consistent metric terms, W(kg) = density(g/cm³) × area(mm²) × length(mm) / 1,000,000.

How do I find the cross-section area of a round bar?

A round (solid) bar has area A = π/4 · d², where d is the diameter. A 25 mm bar therefore has A = 0.7854 × 25² ≈ 490.9 mm². For a tube, subtract the bore: A = π/4 · (OD² − ID²).

What density should I use for steel?

Use 7.85 g/cm³ for plain carbon and low-alloy steel. Stainless is heavier at about 8.0 g/cm³, cast iron lighter at about 7.2 g/cm³, aluminium 2.70 and titanium (Ti-6Al-4V) just 4.43 g/cm³.

Last reviewed: 2026-05-29.