Metal weight calculation is one of the most practical tasks in a machine shop or fab shop. Whether you are quoting a job, planning a crane lift, or checking shipping weight, knowing the density of your material and how to apply it to a cross-section is essential. This guide explains densities for common alloys, the weight formulas for standard stock shapes, and the common mistakes that lead to costly errors.
Pure elements have fixed densities, but alloys vary depending on composition. Steel alloys range from about 0.282 to 0.295 lb/in³ (7.8–8.2 g/cm³) depending on carbon content and alloying elements. Stainless steel is denser than mild steel because of chromium and nickel additions. Aluminum alloys range from 0.095 to 0.102 lb/in³ (2.6–2.8 g/cm³) — 6061 is 0.0975 lb/in³. Titanium at 0.161 lb/in³ (4.46 g/cm³) is about 45% lighter than steel but 65% heavier than aluminum. Copper at 0.324 lb/in³ (8.97 g/cm³) is the densest common engineering metal except for lead and tungsten.
Mild steel (A36, 1018): 0.2833 lb/in³ / 7.85 g/cm³. Stainless steel (304, 316): 0.2875 lb/in³ / 7.96 g/cm³. Aluminum (6061-T6): 0.0975 lb/in³ / 2.70 g/cm³. Copper (C110): 0.324 lb/in³ / 8.97 g/cm³. Brass (C260, C360): 0.3065 lb/in³ / 8.49 g/cm³. Cast iron (gray, ASTM A48): 0.260 lb/in³ / 7.20 g/cm³. Titanium (Grade 5, Ti-6Al-4V): 0.161 lb/in³ / 4.46 g/cm³. These values are standard industry references. Actual density varies ±1–2% depending on exact alloy composition and heat treatment.
Round bar (rod): Weight = π/4 × diameter² × length × density. Example: 1" diameter steel rod, 12" long: π/4 × 1² × 12 × 0.2833 = 2.67 lb. Square bar: Weight = side² × length × density. Example: 1"×1" steel square bar, 12" long: 1 × 12 × 0.2833 = 3.40 lb. Flat bar: Weight = width × thickness × length × density. Hex bar: Weight = (3√3/2) × (across-flats/2)² × length × density. Round tube: Weight = π/4 × (OD² − ID²) × length × density. Plate/sheet: Weight = width × length × thickness × density.
Job quoting: Accurate weight calculation prevents under-quoting material costs. Steel at $0.80/lb versus titanium at $15/lb — a 10× density difference means the same shape can cost 130× more in titanium. Crane and rigging: Always calculate lifting weight before rigging. A 2" diameter steel bar 10 feet long weighs 107 lb — easily lifted by hand. The same bar in copper weighs 122 lb. A 4" bar the same length weighs 427 lb in steel. Shipping: Freight rates are often weight-based. Knowing the exact weight of a machined part avoids surprise freight costs. Stock selection: When weight matters (aerospace, motorsport), switching from steel to aluminum saves about 65% weight for the same volume.
Error 1: Using diameter instead of radius in round bar formula. The formula uses radius squared (r² = (d/2)²), not diameter squared. Error 2: Forgetting unit consistency. If density is in lb/in³, all dimensions must be in inches. If you measure length in feet, convert to inches first. Error 3: Using nominal vs actual dimensions. A 1" round bar is usually 1.000" diameter. But a 1" pipe has a specific OD that is NOT 1" — a 1" Schedule 40 pipe is 1.315" OD. Always verify actual dimensions for pipe. Error 4: Ignoring wall thickness for tubes. A 2" OD tube with 0.125" wall has an ID of 1.75", not 2". Always calculate using (OD² − ID²).
Standard density values are accurate to within about 1–2% for most common alloys. For engineering calculations where precision matters, use the density specification from your material certification (cert sheet). For job quoting and weight estimation, standard reference values are sufficiently accurate. The bigger source of error is usually dimensional tolerance on the stock, not density variation.
Heat treatment causes very small density changes — typically less than 0.5%. Quenching and tempering steel, annealing aluminum, or aging titanium do not meaningfully change the weight of a part. The density values in standard references apply regardless of heat treat condition. The dimensional changes from heat treatment (distortion, growth) are a much larger practical concern than the density change.
Theoretical weight is calculated from dimensions and density. Actual weight can vary due to dimensional tolerances on the stock (typically ±1–3% on hot-rolled bar), surface condition (scale on hot-rolled adds slight weight), and actual alloy composition variation. For most applications, theoretical weight is adequate. For precision weighing (critical aerospace parts, postal regulation), always weigh the actual piece.