Volume Calculator
Calculate the volume of a sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid, square pyramid or tube — each its own calculator, showing the working.
Sphere
A ball, measured from its centre to its surface.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the radius, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Cone
A circular base tapering to a point.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the base radius and height, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Cube
Six square faces — one measurement is enough.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the edge length, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Cylinder
A circular base pulled straight up — a can, a pipe, a tank.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the base radius and height, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Rectangular Tank
A box — a room, a crate, a sump.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the length and width and height, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Capsule
A cylinder with a hemisphere capping each end.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the base radius and height, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Spherical Cap
A slice off the top of a ball — a dome, a dished end.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the base radius and ball radius and height, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Conical Frustum
A cone with its point cut off — a bucket, a plant pot.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the top radius and bottom radius and height, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Ellipsoid
A squashed or stretched ball, measured along three axes.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the axis 1 and axis 2 and axis 3, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Square Pyramid
A square base rising to a point.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the base edge and height, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
Tube
A pipe — the outer cylinder less its bore, measured across.
Example
This is a sample result, not your calculation. Enter your own values to replace it.
Enter the outer diameter and inner diameter and length, then calculate the volume.
Your measurements were in different units, so each was converted into the first field's unit before the formula ran.
Check your entries
Changes update automatically.
How to use this calculator
- Find the shape that matches your solid — each one above is its own calculator, so an answer stays on screen while you work out the next.
- Enter each measurement and choose the unit beside it. Every measurement carries its own unit.
- Press that shape's Calculate button.
- Read the volume, reported in the unit of the first field cubed (cubic metres, cubic feet, and so on), with the formula and the substituted numbers shown above it.
Volume formulas for every shape
Volume is always in cubic units. Each shape has its own formula — these are the eleven the calculator solves, in the order they appear above:
| Shape | Formula | Example |
|---|---|---|
| Sphere | 4⁄3 × π × r3 | 4⁄3 × π × 33 ≈ 113.10 |
| Cone | ⅓ × π × r2 × h | ⅓ × π × 32 × 6 ≈ 56.55 |
| Cube | a3 | 33 = 27 |
| Cylinder | π × r2 × h | π × 22 × 5 ≈ 62.83 |
| Rectangular tank | l × w × h | 2 × 3 × 4 = 24 |
| Capsule | 4⁄3 × π × r3 + π × r2 × h | r 2, h 5 ≈ 96.34 |
| Spherical cap | ⅓ × π × h2 × (3R − h) | R 9, h 4 ≈ 385.37 |
| Conical frustum | ⅓ × π × h × (r2 + rR + R2) | r 2, R 4, h 5 ≈ 146.61 |
| Ellipsoid | 4⁄3 × π × a × b × c | 4⁄3 × π × 4 × 6 × 5 ≈ 502.65 |
| Square pyramid | ⅓ × a2 × h | ⅓ × 32 × 5 = 15 |
| Tube | π × (d12 − d22) ÷ 4 × l | d 4 and 1, l 6 ≈ 70.69 |
A worked example
Find the volume of a ball with a radius of 3. The sphere formula is 4⁄3 × π × radius3 = 4⁄3 × π × 33 = 4⁄3 × π × 27 = 36π ≈ 113.10 cubic units. A cylinder with a radius of 2 and a height of 5 is π × radius2 × height = π × 4 × 5 = 20π ≈ 62.83 cubic units — simply its circular base area multiplied by how tall it is.
The one-third pattern
Two of these formulas share a neat relationship. A cone holds exactly one third of the cylinder that would enclose it, and a square pyramid holds one third of its enclosing box — both have the same base and height as the fuller shape. That is why the cone and pyramid formulas are just the cylinder and tank formulas with a ⅓ in front.
How the capsule is built
A capsule is a cylinder with a hemisphere capped on each end — a pill shape. Its volume is the cylinder plus a full sphere (the two hemispheres together), which is why the formula reads 4⁄3 × π × r3 + π × r2 × h. Here the height is only the straight cylindrical section, not the rounded caps. With a radius of 2 and a cylinder height of 5, that is 4⁄3 × π × 8 + π × 4 × 5 ≈ 96.34 cubic units.
The spherical cap needs only two of its three values
A spherical cap is a slice off the top of a ball, and its base radius, the ball's radius and the cap's height are not independent — give any two and the third follows. Enter a base radius and a ball radius, though, and there are two answers: a chord cuts a ball twice, so the same base circle bounds a shallow cap and a deep one. The calculator solves h = R ± √(R² − r²) and works both through, which is why that one shows two volumes where every other shape shows one.
Keep your units consistent
Because volume multiplies three lengths, the units cube: metres give cubic metres, feet give cubic feet. Every measurement must reach the formula in the same unit, so each one is converted into the unit of the first field for you — enter a radius in metres first and the answer is in cubic metres, whatever the later fields were measured in. If you need capacity rather than raw volume, remember the standard conversions — one cubic metre is 1,000 litres, and one cubic foot is about 7.48 US gallons.
Everyday uses
Volume calculations help with shipping and packaging, filling a pool or tank, cooking, and construction. For pouring a concrete slab, the concrete calculator converts volume into cubic yards and bags. For flat areas rather than solids, see the area calculator.
Frequently asked questions
How do I calculate volume?
Use the calculator for your shape and enter its dimensions. A rectangular tank is length × width × height; a sphere is 4⁄3 × π × radius³; a cylinder is π × radius² × height. Each one shows the formula, the formula with your numbers in it, and the answer.
How do I find the volume of a cylinder?
Volume = π × radius² × height. A cylinder with radius 2 and height 5 has a volume of π × 4 × 5 ≈ 62.83 cubic units. It is simply the circular base area (π × r²) multiplied by the height.
How do I find the volume of a sphere?
Volume = 4⁄3 × π × radius³. A sphere of radius 3 has a volume of 4⁄3 × π × 27 ≈ 113.10 cubic units. Only the radius matters — a sphere has no other dimension.
How do I find the volume of a cone?
Volume = ⅓ × π × radius² × height — exactly one third of a cylinder with the same base and height. A cone with radius 3 and height 6 holds ⅓ × π × 9 × 6 ≈ 56.55 cubic units.
How do I find the volume of a rectangular prism?
A rectangular prism (a box) is length × width × height. A box 2 × 3 × 4 has a volume of 24 cubic units. Use the Rectangular Tank calculator above and enter the three dimensions.
What units is the volume in?
Every measurement has its own unit, so you can mix metres and centimetres freely. Each is converted into the unit of the first field, and the volume is reported in that unit cubed — enter a radius in metres first and the answer is in cubic metres.
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About this calculator
Method reviewed for accuracy on July 25, 2026
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