Math
Volume Calculator
Choose a solid, enter its dimensions, and the volume calculator returns the volume in cubic units, the exact answer in terms of π where one exists, the surface area, and the capacity in liters and US gallons.
It covers cubes, boxes, cylinders, cones, spheres, hemispheres, pyramids, triangular prisms, ellipsoids, capsules, and cone frustums.
Pick the solid; the dimension fields update to match its formula.
Lengths use this unit; volume is in cubic units and is also converted to liters and US gallons.
The perpendicular height, straight up from the base — not the slant.
Half the diameter. For a frustum this is the larger (bottom) radius.
Try an example
Result
Volume
—
- Volume with units
- —
- Surface area
- —
- Liters
- —
- US gallons
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
Volume formulas for every solid on this page
| Solid | Volume formula | Notes |
|---|---|---|
| Cube | V = s³ | s = edge |
| Rectangular prism (box) | V = l × w × h | any box-shaped object |
| Cylinder | V = πr²h | base area × height |
| Cone | V = ⅓πr²h | one third of the matching cylinder |
| Sphere | V = (4/3)πr³ | r = radius |
| Hemisphere | V = (2/3)πr³ | half a sphere |
| Rectangular pyramid | V = ⅓ l w h | one third of the matching box |
| Triangular prism | V = ½ b h × L | triangle area × length |
| Ellipsoid | V = (4/3)πabc | a, b, c = semi-axes |
| Capsule | V = πr²L + (4/3)πr³ | cylinder plus two hemispheres |
| Cone frustum | V = ⅓πh(R² + Rr + r²) | R, r = bottom and top radii |
Cubic units, liters, and gallons
Volume counts how many unit cubes fill a solid, so it is measured in cubic units (cm³, in³, ft³). Because 1 liter is exactly 1,000 cm³ and 1 US gallon is 3.785411784 liters, any volume in a real length unit can be turned into a capacity: a 10 × 10 × 10 cm box holds exactly 1 L. The calculator does that conversion whenever you pick a real unit.
| 1 cubic unit | Liters | US gallons |
|---|---|---|
| 1 cm³ | 0.001 L | 0.000264 gal |
| 1 in³ | 0.016387 L | 0.004329 gal |
| 1 ft³ | 28.3168 L | 7.4805 gal |
| 1 m³ | 1000 L | 264.172 gal |
How to use it
- Select the solid that matches your object.
- Enter each dimension in the same unit and pick that unit. Radius is half the diameter; height is measured straight up, not along a slant.
- Read the volume and, for round solids, the The answer kept as a fraction or radical instead of a rounded decimal. in terms of π.
- Use the liters/gallons line for containers, and the surface area line for painting, wrapping, or material estimates.
How to read the answer
A cylinder with radius 3 and height 8 shows 72π cm³ (226.1947 cm³): the first is the exact value most math classes want, the second is the measurement you would actually use. The interpretation sentence restates the volume as a count of unit cubes and, when a real unit is chosen, as a container capacity.
Common mistakes and edge cases
- Using the diameter where the formula wants the radius. Halve the diameter first; otherwise the volume is 4× too large for cylinders and 8× too large for spheres.
- Forgetting the ⅓ for cones and pyramids — they hold exactly one third of the cylinder or box with the same base and height.
- Using the slant height of a cone or pyramid instead of the vertical height.
- Mixing units (radius in inches, height in feet). Convert everything to one unit before entering it.
- Zero or negative dimensions are rejected; a capsule with cylinder length 0 is allowed and becomes a sphere.
Worked examples
Cylinder r = 3, h = 8 (72π)
Volume
226.1947
Cube edge 4
Volume
64
Box 10 × 6 × 4
Volume
240
Cone r = 3, h = 8 (24π)
Volume
75.3982
Sphere r = 3 (36π)
Volume
113.0973
Hemisphere r = 3 (18π)
Volume
56.5487
Square pyramid 6 × 6 base, height 4
Volume
48
Triangular prism, decimal dimensions
Volume
11.25
Capsule r = 2, L = 10
Volume
159.174
Frustum R = 4, r = 2, h = 6 (56π)
Volume
175.9292
Zero height cylinder (impossible)
Volume
—
Frequently asked questions
How do I find the volume of a cylinder?+
Multiply the area of the circular base by the height: V = πr²h. A can with radius 3 cm and height 8 cm holds 72π ≈ 226.19 cm³, which is about 0.226 liters.
Why is a cone one third of a cylinder?+
A cone with the same base and height as a cylinder holds exactly one third as much — you can pour three cones of water into the cylinder to fill it. The same is true for a pyramid inside a box.
How do I convert volume to liters?+
Compute the volume in cm³ and divide by 1000 (1 L = 1000 cm³). For cubic inches multiply by 0.016387; for cubic feet multiply by 28.3168. The calculator does this automatically when you pick a real unit.
What is the difference between volume and surface area?+
Volume is the space inside (cubic units); surface area is the total area of the outside faces (square units). A 4 cm cube has volume 64 cm³ and surface area 6 × 16 = 96 cm².
What is a frustum?+
A frustum is a cone (or pyramid) with the top sliced off parallel to the base — the shape of a bucket or lampshade. Its volume is ⅓πh(R² + Rr + r²) using both radii.
Does the sphere formula use radius or diameter?+
Radius. V = (4/3)πr³. If you have the diameter, halve it first: a ball 6 cm across has r = 3 and volume 36π cm³.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Surface Area Calculator
Find the total surface area of a cube, box, cylinder, cone, sphere, rectangular pyramid, or triangular prism with the formula for each solid, the lateral and base breakdown, exact π forms, and square-unit labels.
Cylinder Calculator
Cylinder calculator for volume, lateral area, total surface area, and diagonal from radius and height — or solve the height or radius from a known volume or lateral area. Exact π answers plus liters and gallons.
Cone Calculator
Cone calculator: from radius and height (or slant height, diameter, or volume) get the volume, slant height, lateral and total surface area, apex angle, and base angle with exact π answers and steps.
Sphere Calculator
Enter one sphere measurement — radius, diameter, circumference, surface area, or volume — and get all five with exact π forms (36π), the great-circle area, steps, and liters or gallons of capacity.
Cube Calculator
Enter one cube measurement — edge, face diagonal, space diagonal, surface area, or volume — and get all five, with exact radicals (s√2, s√3), face area, inscribed and circumscribed sphere radii, and liters.
Cylinder Volume Calculator
Calculate cylinder volume, base area, and lateral surface area from radius and height.
Last updated: September 4, 2026