Quick Answer
A volume calculator finds the 3D space inside a shape from its measurements: for a box, volume = length × width × height; for a sphere, V = 4⁄3 π r³; for a cylinder, V = π r² h. Enter your dimensions in any length unit (from millimeters to miles) and read the result instantly in cubic units, liters, or gallons.
Volume Formulas for Every Shape
Volume measures the space a solid occupies, in cubic units. Each shape has its own formula built from its dimensions — a length, a radius, or a set of axes. This calculator covers the ten shapes below and converts the answer to any volume unit you need.
V = l × w × h · Sphere: V = 4⁄3 π r³ · Cylinder: V = π r² h| Shape | Volume formula | You measure |
|---|---|---|
| Box (cuboid) | V = l × w × h | length, width, height |
| Cube | V = a³ | edge a |
| Sphere | V = 4⁄3 π r³ | radius r |
| Cylinder | V = π r² h | radius r, height h |
| Cone | V = 1⁄3 π r² h | radius r, height h |
| Cone frustum | V = 1⁄3 π h (R² + R·r + r²) | radii R & r, height h |
| Capsule | V = π r² (a + 4⁄3 r) | radius r, side a |
| Ellipsoid | V = 4⁄3 π a·b·c | semi-axes a, b, c |
| Square pyramid | V = 1⁄3 a² h | base edge a, height h |
| Tube / pipe | V = π h (R² − r²) | outer R, inner r, length h |
How to Use the Volume Calculator
- Pick your shape.
Tap a shape — box, sphere, cylinder, cone and seven more. Only the fields that shape needs appear, so there’s nothing extra to fill in.
- Enter each measurement and its unit.
Type a number in every field and choose its unit beside it — any length from millimeters to miles. You can even mix units between fields.
- Choose how to show the result.
Pick the output unit (liters, US gallons, cubic feet, m³, and more). The volume updates instantly and also lists the most common conversions.
Worked Examples: Box, Cylinder, Sphere & Cone
| Shape | Dimensions | Formula | Volume |
|---|---|---|---|
| Box | 50 × 40 × 30 cm | l × w × h | 60,000 cm³ = 60 L |
| Cylinder | r = 10 cm, h = 20 cm | π r² h | 6,283 cm³ ≈ 6.28 L |
| Sphere | r = 10 cm | 4⁄3 π r³ | 4,189 cm³ ≈ 4.19 L |
| Cone | r = 10 cm, h = 20 cm | 1⁄3 π r² h | 2,094 cm³ ≈ 2.09 L |
Example math for the cylinder: V = π × r² × h = π × 10² × 20 = π × 2,000 ≈ 6,283 cm³, and since 1,000 cm³ = 1 liter, that is about 6.28 L.
