3D solid volume and surface area calculator

Formula

How it works

These come directly from the standard formulas for each solid: a sphere needs only its radius; a cylinder and cone also need a height, and a cone's surface area needs its slant height, found with the Pythagorean theorem from the radius and height.

Worked example

The same calculation with the default values:

• Shape Sphere
• Radius 4
• Height (ignored for a sphere) 10

1. V = (4/3) × π × 4³ = 268.082573
2. SA = 4 × π × 4² = 201.06193

Result: Volume: 268.08257311 · Surface area: 201.06192983

Common mistakes

• Using diameter instead of radius - every formula here uses radius (r); entering a diameter value directly inflates volume by a factor of 8 and surface area by a factor of 4.
• Mixing up which solid's formula applies - sphere, cylinder, and cone have structurally different volume formulas, and choosing the wrong one for the actual shape gives a completely wrong result, not just an approximation.
• Forgetting that surface area and volume have different units (area in length², volume in length³) - a result reported in the wrong unit power is a sign of a units error, not a legitimate answer.