Formula
rectangle: A = l × w; triangle: A = ½bh; trapezoid: A = ½(a + b)hcuboid: V = lwh; cube: V = s³; cylinder: V = πr²hcone: V = ⅓πr²h; sphere: V = (4/3)πr³
- Surface areas: cuboid 2(lw + lh + wh), cylinder 2πr(r + h), cone πr(r + l), sphere 4πr²
- Cone slant height l = √(r² + h²)
Each shape has its own formula; the calculator picks the right one.
Worked examples
Cylinder, radius 3 and height 10
- Shape
- Cylinder
- Radius
- 3
- Height
- 10
- Unit
- cm
Volume
282.743339 cm³
Curved surface area: 188.495559 cm²
Total surface area: 245.044227 cm²
Cuboid 10 × 4 × 5
- Shape
- Cuboid (rectangular box)
- Length
- 10
- Width
- 4
- Height
- 5
- Unit
- m
Volume
200 m³
Surface area: 220 m²
Space diagonal: 11.874342 m
How it works
Area measures a flat surface in square units and volume measures a solid in cubic units. Pick a shape and enter its dimensions: for a cylinder of radius 3 and height 10 the volume is π × 3² × 10 ≈ 282.74 and the total surface area is 2π × 3 × (3 + 10) ≈ 245.04. Every result is shown with the working so you can follow the formula.
For a triangle or parallelogram the height must be the perpendicular distance from the base, not the length of a slanted side. For a cone the slant height is derived from the radius and height using Pythagoras, and is used for the curved surface area. Choose a unit to label the results; the calculator does not convert between units, so all measurements must use the same one.
For circles on their own use the Circle Calculator; for triangles given three sides use the Triangle Calculator. To convert the result into another unit use the Area Converter or the Volume Converter.
Assumptions and limits
- Solid, regular shapes in flat (Euclidean) space.
- All dimensions use the same unit; the unit label is only for display.