Volume Calculator
Calculate volume and total surface area for common 3D solids, then convert the result to cubic units, liters, and US gallons.
Volume and surface-area formulas
| Solid | Volume | Total surface area |
|---|---|---|
| Rectangular prism | V = lwh | A = 2(lw + lh + wh) |
| Cube | V = s³ | A = 6s² |
| Cylinder | V = πr²h | A = 2πr(r + h) |
| Cone | V = πr²h ÷ 3 | A = πr(r + √(r²+h²)) |
| Sphere | V = 4πr³ ÷ 3 | A = 4πr² |
| Hemisphere | V = 2πr³ ÷ 3 | A = 3πr², including the circular base |
| Square pyramid | V = b²h ÷ 3 | A = b² + 2b√((b÷2)²+h²) |
| Capsule | V = πr²h + 4πr³ ÷ 3 | A = 2πrh + 4πr² |
Checked examples
| Shape and measurements | Volume | Surface area |
|---|---|---|
| Rectangular prism: 4 × 3 × 2 m | 24 m³ | 52 m² |
| Cube: side 3 m | 27 m³ | 54 m² |
| Cylinder: r=2 m, h=5 m | 20π ≈ 62.8319 m³ | 28π ≈ 87.9646 m² |
| Cone: r=3 m, h=4 m | 12π ≈ 37.6991 m³ | 24π ≈ 75.3982 m² |
| Sphere: r=3 m | 36π ≈ 113.097 m³ | 36π ≈ 113.097 m² |
| Hemisphere: r=3 m | 18π ≈ 56.5487 m³ | 27π ≈ 84.823 m² |
How to use this calculator
- Select the solid shape.
- Choose the unit used for every entered length.
- Enter only the dimensions displayed for that shape.
- Calculate to obtain volume, total surface area, liters, cubic feet, and US gallons.
- Keep full precision for later calculations; round only the final practical result.
Conversions and limits
- 1 m³ = 1,000 liters = 35.3146667 ft³ ≈ 264.172052 US gallons.
- Every dimension must be greater than zero and no greater than 10⁹ selected length units.
- Surface area includes every exposed face; hemisphere area includes its flat circular base.
- The formulas assume ideal geometric solids and do not subtract wall thickness, openings, internal parts, or freeboard.
- For buying concrete, soil, gravel, or other materials, use the specialized calculator that includes waste, density, bags, and purchasing units.
Frequently asked questions
Why is volume measured in cubic units?
Volume multiplies three independent lengths. If each length is measured in meters, the product is cubic meters.
Is surface area the same as volume?
No. Surface area measures the outside covering in square units; volume measures the enclosed three-dimensional space in cubic units.
Does cylinder height include the radius?
No. Enter the straight perpendicular distance between the two circular bases.
What length should I enter for a capsule?
Enter the cylindrical middle section only. The calculator adds the two hemispherical ends, which together form one sphere.
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