Volume, Surface Area and Mass of Solid Shapes Calculator

Volume, surface area and mass of a cylinder, cone, sphere, box, frustum or tube.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Pick a shape and enter its dimensions in millimetres. The calculator gives the volume, the total surface area and, if you enter a density, the mass. Surface areas include the end faces.

It is useful for sizing tanks and hoppers, estimating the paint or coating area, and finding the weight of machined parts. For plate, bar and rolled sections use the steel weight calculator.

Formulas used

  • V_{cylinder} = \frac{\pi D^2 H}{4}
  • V_{cone} = \frac{\pi D^2 H}{12}
  • V_{sphere} = \frac{\pi D^3}{6}
  • m = \rho V

Worked example

With the default numbers in the calculator above:

  1. Volume: 1571 cm³
  2. Total surface area: 785.4 cm²
  3. Mass: 12.33 kg

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is a frustum?

A cone with its top cut off by a plane parallel to the base, like a bucket or a hopper outlet.

How do I find the capacity in litres?

Divide the volume in cubic centimetres by 1000.

What density do I use?

About 7850 kg/m³ for steel, 2700 for aluminium, 1000 for water.

Related calculators

Further reading: Any engineering mathematics handbook.

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