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Area and volume calculator, 16 shapes, with the steps.
Pick a shape, type its sizes and get the area and perimeter of a flat shape, or the volume and surface area of a solid: circle, square, rectangle, triangle, trapezoid, parallelogram, ellipse, sector, ring, cube, box, sphere, cylinder, cone, pyramid and prism. Use mm, cm, m, in, ft or yd, and see the formula, a worked line, a labelled drawing and the answer in the other units.
Flat shapes (area, perimeter)
Solids (volume, surface area)
Numbers like 2.5, 3/4 or sqrt(2) work. All sizes use the same unit.
Worked out in your browser. Nothing is sent anywhere.
Guide
How to find area and volume, with worked examples.
An area and volume calculator turns a few measurements into the area, perimeter, surface area or volume of a shape. Pick a flat shape for its area and perimeter (or circumference), or a solid for its volume and surface area. Type the sizes in millimetres, centimetres, metres, inches, feet or yards, and the answer comes in your unit and the others, with the formula, a worked line and a labelled drawing.
How to use the area and volume calculator
- Pick a shape under Flat shapes or Solids.
- Choose the Unit of length, such as centimetres.
- Type the sizes. For a circle, square, cube or sphere, I know the lets you start from the radius, diameter, diagonal, area or volume instead.
- The big card is the area (flat shapes) or volume (solids). The other cards, the drawing and the unit table update as you type.
- Copy result copies all the answers as one line, and Copy link shares the shape and numbers.
Area formulas for flat shapes
| Shape | Area | Perimeter |
|---|---|---|
| Circle | πr² | 2πr (circumference) |
| Square | s² | 4s |
| Rectangle | l × w | 2(l + w) |
| Triangle | ½ × base × height | a + b + c |
| Trapezoid | ½(a + b) × h | a + b + c + d |
| Parallelogram | base × height | 2(base + side) |
| Ellipse | πab | no simple formula |
| Sector | (θ ÷ 360) × πr² | arc + 2r |
| Ring | π(R² − r²) | 2πR + 2πr |
Volume and surface area of solids
| Solid | Volume | Surface area |
|---|---|---|
| Cube | s³ | 6s² |
| Box | l × w × h | 2(lw + lh + wh) |
| Sphere | (4/3)πr³ | 4πr² |
| Cylinder | πr²h | 2πr(r + h) |
| Cone | (1/3)πr²h | πr(r + l), l = √(r² + h²) |
| Pyramid | (1/3) × base area × h | base + four faces |
| Prism | base area × h | 2 × base + perimeter × h |
Worked example: the area of a circle
A circle with a radius of 5 cm has an area of π × 5² = 25π = 78.54 cm² and a circumference of 2 × π × 5 = 10π = 31.42 cm. The calculator shows both the exact form, 25π, and the decimal. If you only know the diameter, pick Diameter under I know the: a diameter of 10 gives the same circle. If you know the area, say 50 cm², the radius is √(50 ÷ π) = 3.989 cm.
Worked example: the volume of a cylinder
A cylinder with a radius of 3 cm and a height of 10 cm has a volume of π × 3² × 10 = 90π = 282.74 cm³. Its side, the lateral area, is 2π × 3 × 10 = 60π = 188.50 cm². Add the two circular ends, 2 × 9π = 18π, and the surface area is 78π = 245.04 cm². In litres, 282.74 cm³ is 0.28274 L, since 1,000 cm³ is 1 litre.
More examples
- Cone: radius 3 and height 4 give a slant height √(9 + 16) = 5. Volume is (1/3) × π × 9 × 4 = 12π = 37.70. Surface area is π × 3 × (3 + 5) = 24π = 75.40.
- Box: 4 × 3 × 2 has volume 24 and surface area 2 × (12 + 8 + 6) = 52.
- Trapezoid: parallel sides 6 and 10 with height 4 have area ½ × 16 × 4 = 32.
- Sector: radius 6 and angle 60° have area (60 ÷ 360) × π × 36 = 6π = 18.85 and an arc of 2π = 6.28.
Rings, sectors, ellipses, pyramids and prisms
A ring is a big circle with a smaller one cut out, so its area is π(R² − r²). A sector is a slice of a circle, a fraction θ ÷ 360 of its area. An ellipse needs two half-widths, a and b. Its area is πab, and the calculator finds its perimeter with a precise method because there is no simple formula. A pyramid here has a rectangular base and its tip over the centre, and a prism has a regular base with any number of sides from 3 to 100, so a triangular prism uses 3 and a hexagonal one uses 6.
Units, squared and cubed
Area is in square units and volume in cubic units, so converting is not a single factor. 78.54 cm² is 12.17 in², because 1 in = 2.54 cm, and an inch squared is 6.4516 cm². The table under the answer does this for you in all six units, using the exact definitions 1 in = 0.0254 m, 1 ft = 0.3048 m and 1 yd = 0.9144 m (NIST, checked 18 Oct 2026). For other units use the unit converter.
Common mistakes
- Radius or diameter. The radius is half the diameter. Using the diameter as the radius makes a circle's area four times too big.
- Slant height or height. A cone's volume uses the straight up height h. The slant height l is along the side and only goes in the surface area.
- Mixed units. Convert every length to one unit first. 2 m by 50 cm is 2 m by 0.5 m, or 200 cm by 50 cm.
For pouring a slab, the concrete calculator turns a volume into bags. For fractions in a measurement use the fraction calculator.
Questions
Good to know.
How do I find the area of a circle?
Square the radius and multiply by π: A = πr². A radius of 5 gives 25π, which is 78.54. If you have the diameter, halve it first.
How do I find the volume of a cylinder?
Multiply the area of the circular base by the height: V = πr²h. With r = 3 and h = 10 that is 90π, or 282.74.
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.
What is the difference between surface area and volume?
Surface area is the total area of the outside of a solid. Volume is how much fits inside.
Can I work out a radius from the area?
Yes, for a circle: r = √(A ÷ π). Choose Circle, then Area under I know the. A square, cube and sphere work backwards too.
What is the slant height of a cone?
The distance from the tip down the side to the edge of the base, l = √(r² + h²). It is used for the side area, not the volume.
Why is the answer shown as a number of π?
So you can see it exactly. 25π is exact, and 78.54 is that rounded. Both are shown for shapes with a circle in them.
Which units can I use?
Millimetres, centimetres, metres, inches, feet and yards. The table under the result gives the answer in all of them, and volume also in litres.
Is anything sent anywhere?
No. It all runs in your browser, and your last numbers are remembered on this device only.