About Volume Calculator
This volume calculator is free, needs no sign-up and runs in your browser, so your measurements are never uploaded. It handles twelve solids: cube, cuboid, cylinder, cone, sphere, hemisphere, pyramid, prism, cone frustum, capsule, ellipsoid and tube (hollow cylinder). For each it gives the volume and the total surface area with the formula, the substitution and a labelled diagram.
The volume is shown in the cube of the unit you measured in and converted to cubic metres, centimetres, millimetres, inches, feet and yards, and to litres, millilitres, US and imperial gallons, quarts, cups and fluid ounces. That makes it easy to size a tank, a pool or a pipe in the unit you buy it in.
Everything is calculated on your device. The only approximation is the surface area of an ellipsoid, which has no simple exact formula and is marked as approximate.
How to use Volume Calculator
- Choose the solid from the list.
- Enter its dimensions in the boxes, labelled with the measurement each one means.
- Pick the unit you measured in, and the volume unit you want, such as litres or gallons.
- Read the volume, the surface area and the table of every unit.
- Compare the labelled diagram with your object to be sure each number is in the right box.
- Open the step-by-step working to see both formulas filled in with your numbers.
Features
- Twelve solids, each with volume, total surface area, formulas and working.
- A labelled schematic diagram for every solid.
- Eight length units for the inputs.
- Volume in cubic units, litres, millilitres, US and imperial gallons, quarts, cups and fluid ounces.
- Cone frustum, capsule, ellipsoid and hollow tube, which many calculators leave out.
- Regular-polygon prisms with any number of sides from 3 to 1000.
- Helpful messages, such as when an inner radius is not smaller than the outer one.
Volume and surface area formulas
Volume is in the cube of the length unit, so centimetres give cubic centimetres, and surface area is in the square of it. The calculator multiplies the factor of the length unit by itself three times to convert volumes.
Surface area here is the total surface, including the base or bases.
Cube: V = a³, S = 6a²
Cuboid: V = lwh, S = 2(lw + lh + wh)
Cylinder: V = π r² h, S = 2π r (r + h)
Cone: V = ⅓ π r² h, S = π r (r + √(r² + h²))
Sphere: V = 4/3 π r³, S = 4π r²
Hemisphere: V = 2/3 π r³, S = 3π r²
Pyramid: V = ⅓ l w h
Frustum: V = π h (R² + R r + r²) / 3
Capsule: V = π r² h + 4/3 π r³
Ellipsoid: V = 4/3 π a b c
Tube: V = π (R² − r²) hWorked examples
Cylinder, radius 3 cm, height 10 cm gives V = 282.7433 cm³
π × 3² × 10 = 90π, about 0.2827 litres. Surface area 245.0442 cm².
Sphere, radius 3 gives V = 113.0973
4/3 × π × 27 = 36π. The surface area is the same number, 113.0973, for this radius.
Cone, radius 3, height 4 gives V = 37.6991
The slant height is 5, so the surface area is π × 3 × (3 + 5) = 75.3982.
Tank: cylinder, radius 1.2 m, height 3 m gives 13571.68 litres
About 3585.2586 US gallons.
Volume units in millilitres
| Unit | Millilitres in one |
|---|---|
| Cubic metres (m³) | 1000000 |
| Cubic centimetres (cm³) | 1 |
| Cubic millimetres (mm³) | 0.001 |
| Cubic inches (in³) | 16.387064 |
| Cubic feet (ft³) | 28316.847 |
| Cubic yards (yd³) | 764554.86 |
| Litres (l) | 1000 |
| Millilitres (ml) | 1 |
| US gallons | 3785.4118 |
| Imperial (UK) gallons | 4546.09 |
| US quarts | 946.35295 |
| US cups | 236.58824 |
| US fluid ounces | 29.57353 |
Good to know
Gallons: US or imperial
A US gallon is 3.785411784 litres and an imperial (UK) gallon is 4.54609 litres, so the two differ by about 20%. Both are listed. Check which one your product label uses.
Ellipsoid surface area
The surface area of a general ellipsoid has no elementary closed form. This calculator uses Knud Thomsen’s formula with p = 1.6075, which is within about 1.1% of the true value. When two or three semi-axes are equal the shape is a sphere or a spheroid and the formula is exact or very close.
Privacy: how it works
- All the calculations run in your browser tab. The dimensions you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Use the inside dimensions when you want the capacity of a container, and the outside ones for the space it takes up.
- For a pyramid with a square base, enter the same number for length and width.
- A capsule is a cylinder with a hemisphere on each end. Enter the cylinder length only, not the overall length.
- To fill a tank to part of its height, enter that height instead of the full height.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your measurements are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your measurements are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I calculate the volume of a cylinder?
Multiply the area of the circular base by the height: V = π r² h. For radius 3 and height 10 that is 90π, about 282.74.
What is the volume of a sphere?
V = 4/3 π r³. A sphere of radius 3 holds 36π, about 113.10 cubic units.
How do I convert cubic metres to litres?
One cubic metre is 1000 litres. Select litres as the output unit and the calculator does the conversion from whichever length unit you used.
What is a frustum?
A frustum is a cone with its top cut off by a plane parallel to the base. It has two radii, R at the bottom and r at the top, and a height.
How is a hemisphere different from a sphere?
It is half a sphere, so the volume is half. Its total surface area is 3π r²: half the sphere’s curved area plus the flat circular face.
Does surface area include the base?
Yes. It is the total surface area, so cones, cylinders and pyramids include their bases.
How do I find the volume of a hollow pipe?
Use the tube solid with the outer radius, inner radius and length. The volume is the material volume: π (R² − r²) times the length. Use the cylinder with the inner radius for the space inside.
Popular Volume Calculator pages
- Cylinder Volume CalculatorEnter the radius and height of a cylinder.
- Sphere Volume CalculatorEnter the radius of a sphere.
- Cone Volume CalculatorEnter the radius and height of a cone.
- Cube Volume CalculatorEnter the edge of a cube.
- Cuboid Volume CalculatorEnter the length, width and height of a box.
- Box Volume CalculatorEnter the inside length, width and height of a box.
- Pyramid Volume CalculatorEnter the base length, base width and height of a pyramid.
- Hemisphere Volume CalculatorEnter the radius of a hemisphere.
- Prism Volume CalculatorEnter the number of base sides, the side length and the prism height.
- Frustum Volume CalculatorEnter the bottom radius, top radius and height of a truncated cone.
- Capsule Volume CalculatorEnter the radius and the length of the cylindrical part.
- Ellipsoid Volume CalculatorEnter the three semi-axes of an ellipsoid.
- Pipe Volume CalculatorEnter the outer radius, inner radius and length of a pipe.
- Tank Volume CalculatorEnter the inside radius and height of a cylindrical tank.