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Surface Area Calculator

Surface area of ten solids, with the formula shown.

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The formula

—

Breakdown

PartAreaShare

Total surface area

—

Related values

Lateral surface area—
Base area—
Volume—
Area ÷ volume—

—

Radius of a sphere with the same volume

Units are yours — enter everything in the same unit and the area comes out squared, the volume cubed. Lateral area excludes the base or bases; total area includes them. Surface-area-to-volume ratio governs heat exchange, which is why small objects cool faster.

Quick Tool Overview

The Surface Area Calculator handles ten common solids — sphere, cube, cuboid, cylinder, cone, pyramid, prism, hemisphere, capsule and torus — printing the formula with your dimensions substituted in, and breaking lateral area out from total.

What it does
Calculates surface area and volume for ten solids
You give it
A shape and the dimensions it needs
You get back
Total, lateral and base areas, plus volume
Best for
Geometry homework, packaging and materials estimates
Calculators Free, unlimited use No sign-up Runs in your browser

About the Surface Area Calculator

Work out the surface area of ten common solids — sphere, cube, cuboid, cylinder, cone, square pyramid, triangular prism, hemisphere, capsule and torus — with the formula printed alongside and your own dimensions substituted into it.

Where a solid has both a curved and a flat part, the two are reported separately as well as together, because questions often want the lateral area rather than the total: painting the side of a cylindrical tank is a different quantity from painting the whole thing including its ends. Volume is calculated at the same time, along with the surface-area-to-volume ratio, which is the figure that matters in heat transfer and in biology.

Key features of the Surface Area Calculator

Ten solids covered

From the everyday cube and cylinder through to the capsule and torus.

Lateral separated from total

Painting the side of a tank is a different quantity from painting the whole thing, and the tool reports both.

Volume alongside

Calculated at the same time, since questions rarely ask for only one of the two.

Surface-area-to-volume ratio

The figure that governs heat exchange and explains why cells stay small.

Formula shown substituted

Each result prints its formula with your own numbers in it, ready to copy into working.

How to use the Surface Area Calculator

  1. 1

    Pick a solid

    Ten shapes are supported, each with the dimensions it actually needs.

  2. 2

    Enter the dimensions

    Radius, height, edge length or whatever the shape requires. Units are yours.

  3. 3

    Read the areas

    Total surface area, plus lateral and base areas broken out separately.

  4. 4

    Check the extras

    Volume and the surface-area-to-volume ratio are calculated at the same time.

Frequently asked questions

4πr², which is exactly four times the area of a circle of the same radius. Its volume is (4/3)πr³.

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