Circle of radius 7 cm
Area 153.94 cm², circumference 43.98 cm.
Area and volume calculator
Every length is in the unit you pick, so area comes out in square units and volume in cubic units. π is 3.14159265. Circular and round shapes use the radius, not the diameter.
Unit
Area
50 cm²
- Perimeter
- 30 cm
- Diagonal
- 11.18 cm
The shape formulas you actually use
Most area and volume problems at home or in school use the same eight shapes. Each has a short formula, and the main error is mixing units or using the diameter for the radius.
A rectangle of 10 by 5 cm has an area of 50 cm² and a perimeter of 30 cm. A circle with a radius of 7 cm has an area of about 153.94 cm² and a circumference of 43.98 cm. A cylinder with a radius of 3 and height of 10 holds about 282.74 cubic units. A cone with the same radius and a height of 4 holds about 37.70. A sphere of radius 3 holds about 113.10.
To get area in square metres from feet, multiply by 0.0929. To get litres from cubic centimetres, divide by 1,000. These conversions come up in the paint, tile and concrete calculators here.
For a flat shape the answer is in square units, for a solid in cubic units. The tool prints the right unit, so a mismatched answer is a sign that one measurement was entered in another unit.
Sources
What this calculator does not account for
- Irregular shapes.
- Wall thickness for hollow solids.
- Rounding in π.
How this is calculated
Formula: Standard area and volume formulas
rectangle ab; triangle ½bh; circle πr²; cuboid abc; cylinder πr²h; cone ⅓πr²h; sphere 4⁄3πr³What the symbols mean
- rRadius, half the diameter.
- hHeight or length along the axis.
Good to know
- π is taken as 3.14159265.
- Units follow your choice, so cm gives cm² for area and cm³ for volume.
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Worked examples
Each example is worked out by the same code as the calculator above.
Cylinder, radius 3 and height 10
Volume 282.74 cubic units.
Embed this calculator
The frame shows the tool only.
<iframe src="/embed/area-volume-calculator" title="Area and volume" width="100%" height="720" style="border:0;max-width:42rem" loading="lazy"></iframe>Questions
What is the difference between area and volume?
Area measures a flat surface in square units. Volume measures the space inside a solid in cubic units.
Do I enter radius or diameter?
Radius. If you have the diameter, halve it.
How do I convert cm² to m²?
Divide by 10,000, since 100 cm × 100 cm makes one square metre.
How is the trapezium area found?
Average the two parallel sides and multiply by the height between them.