Volume Calculator
Choose a solid, enter its dimensions and read the volume in cubic units, liters, gallons and cubic yards, with surface area and a labelled drawing.
V = πr²h
- Surface area
- 207.345 ft²
- Base area = π × 3² = 28.2743 ft²
- V = base × h = 28.2743 × 8 = 226.195 ft³
Volume in other units
| m³ | 6.4051 |
| liters | 6,405.12 |
| ft³ | 226.195 |
| yd³ | 8.3776 |
| in³ | 390,864 |
| US gallons | 1,692.05 |
| cm³ (mL) | 6,405,120 |
Volume formulas
| Solid | Volume | Surface area |
|---|---|---|
| Cube | V = s³ | SA = 6s² |
| Rectangular prism (box) | V = l × w × h | SA = 2(lw + lh + wh) |
| Cylinder | V = πr²h | SA = 2πr(r + h) |
| Sphere | V = ⁴⁄₃ πr³ | SA = 4πr² |
| Hemisphere | V = ⅔ πr³ | SA = 3πr² |
| Cone | V = ⅓ πr²h | SA = πr(r + √(r² + h²)) |
| Square pyramid | V = ⅓ b²h | SA = b² + 2b√((b/2)² + h²) |
| Triangular prism | V = ½ × b × t × l | SA = bt + l(b + 2s) |
The pattern behind every formula
Prisms and cylinders — solids with the same cross-section all the way up — are base area × height. Solids that taper to a point, cones and pyramids, hold exactly one third of that. A sphere holds two thirds of the cylinder that wraps it.
Three cones fill one cylinder
Take a cone and a cylinder with the same round base and the same height. Pour the cone full of water into the cylinder three times and it's full — which is why the cone formula is ⅓ πr²h. The same ⅓ links a pyramid to the box around it.
Cylinder is ⅓ full
Questions people ask
How do you calculate volume?
For boxes multiply length × width × height. For cylinders multiply the circle area πr² by the height. For cones and pyramids take one third of base area × height. For spheres use ⁴⁄₃πr³.
How do I convert cubic feet to gallons?
Multiply by 7.48052 for US gallons (or 6.229 for imperial gallons).
How many liters are in a cubic meter?
Exactly 1,000 liters. One liter is the volume of a 10 cm cube.
What is the difference between volume and capacity?
Volume is the space an object takes up; capacity is how much a container can hold. For thin-walled containers they are about equal; for thick walls, measure the inside dimensions.
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