Math
Volume Calculator
Pick a 3D shape, enter its dimensions, and get its volume — plus surface area for the shapes where a standard formula exists.
Calculation inputs
Choose a shape first; the three dimension boxes map to that shape as described below.
Results
No result yet
Complete the fields and select Calculate to show results here.
About this calculator
This tool finds the volume of six common 3D solids — cube, rectangular box, cylinder, sphere, cone, and triangular prism — and the surface area for the shapes where a standard formula applies. It suits students checking homework, DIYers sizing a container, and anyone who needs a quick geometric answer.
How the calculation works
- Cube: V = a³, SA = 6a²
- Box: V = lwh, SA = 2(lw + lh + wh)
- Cylinder: V = πr²h, SA = 2πr² + 2πrh
- Sphere: V = (4/3)πr³, SA = 4πr²
- Cone: V = (1/3)πr²h, SA = πr² + πr√(r² + h²)
- Triangular prism: V = (1/2) × base × triangle height × length
Notes and assumptions
Volume measures the space inside a solid; surface area measures the skin around it. Both use the same length unit you enter.
For cones and cylinders the height is the straight vertical height, not the slant length.
How it works in plain English
Every volume formula reduces a solid to a small set of measurements: edges for straight-sided shapes, a radius and height for round ones. You pick the shape first, then enter its dimensions in the order described under each box. The tool applies the matching formula and reports the volume in cubic units of whatever you measured in.
For the cube, box, cylinder, sphere, and cone it also computes surface area — the total area of the skin around the solid. The cone's surface area uses the slant height, which it derives from the radius and vertical height with the Pythagorean theorem.
The triangular prism is the exception: its surface area depends on all three sides of the triangular face, which two measurements cannot fix, so only its volume is shown. All formulas come from standard geometry and assume perfect, regular shapes.
The formula
- Cube: V = a³, SA = 6a²
- Box: V = lwh, SA = 2(lw + lh + wh)
- Cylinder: V = πr²h, SA = 2πr² + 2πrh
- Sphere: V = (4/3)πr³, SA = 4πr²
- Cone: V = (1/3)πr²h, SA = πr² + πr√(r² + h²)
- Triangular prism: V = (1/2) × base × triangle height × length
Worked example
Suppose you want the volume of a cylindrical storage tank with a radius of 3 feet and a height of 5 feet.
Select the cylinder, enter 3 as the radius and 5 as the height. The volume is π × 3² × 5, which is about 141.37 cubic feet.
The surface area is 2π × 3² + 2π × 3 × 5, about 150.80 square feet — useful if you were pricing paint for the tank. Since one cubic foot holds about 7.48 US gallons, the tank holds roughly 1,057 gallons.
Volume formulas at a glance
| Shape | Volume | Surface area |
|---|---|---|
| Cube (side a) | a³ | 6a² |
| Box (l × w × h) | lwh | 2(lw + lh + wh) |
| Cylinder (r, h) | πr²h | 2πr² + 2πrh |
| Sphere (r) | (4/3)πr³ | 4πr² |
| Cone (r, h) | (1/3)πr²h | πr² + πr√(r² + h²) |
| Triangular prism | (1/2) × b × hₜ × l | depends on all three triangle sides |
Source: standard Euclidean geometry formulas, as found in any geometry textbook or reference such as Wolfram MathWorld.
Frequently asked questions
What units does the result come in?
Whatever unit you measured in, cubed. Enter dimensions in centimetres and the volume is in cubic centimetres; enter feet and it is cubic feet. Mixing units — say, radius in inches and height in feet — gives a meaningless answer, so convert everything to one unit first.
Why is there no surface area for the triangular prism?
The surface area of a triangular prism needs the lengths of all three sides of the triangular face, but the volume only needs the triangle's base and height. Two measurements cannot determine three sides, so the tool shows volume only rather than guessing.
Is the cone's height the vertical height or the slant?
Enter the vertical height — the straight distance from the tip to the centre of the base. The tool works out the slant height itself using √(r² + h²) when it computes the surface area.
How do I convert the volume to gallons or litres?
One cubic foot is about 7.48 US gallons, and one cubic metre is 1,000 litres. For cubic centimetres, divide by 1,000 to get litres. You can also use the Unit Converter on this site to convert the result directly.
Can I use this for irregular shapes?
Not directly — the formulas assume perfect solids. For an irregular object, break it into simple shapes, run each one, and add the volumes. For a real object you can also submerge it in water and measure the displaced volume.
Helpful next steps
- Concrete Calculator — Estimate concrete for slabs, footings and columns, including bags.
- Volume Converter — Convert the result between cubic units, liters and gallons.
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