The Volume of a Shape Calculator calculates how much space a 3D shape holds, using the standard volume formula for each solid — base area × height for prisms and cylinders, one-third of that for cones and pyramids, and (4/3)πr³ for spheres.
Choose from nine shapes, enter the dimensions in any unit, and show the result in cubic centimeters, cubic meters, liters, US gallons, cubic feet and more.
Volume of a Shape Calculator
Volume of cubes, boxes, cylinders, spheres, cones, pyramids, prisms, hemispheres and ellipsoids — in cm³, m³, litres, gallons and more.
Formula
| Shape | Volume |
|---|---|
| Cube | V = a³ |
| Box (rectangular prism) | V = l × w × h |
| Cylinder | V = πr²h |
| Sphere | V = (4/3)πr³ |
| Cone | V = πr²h ÷ 3 |
| Square pyramid | V = a²h ÷ 3 |
| Triangular prism | V = ½ × b × h × L |
| Hemisphere | V = (2/3)πr³ |
| Ellipsoid | V = (4/3)πabc |
Where: a = side, l/w/h = length/width/height, r = radius, b and h (prism) = triangle base and height, L = prism length, a/b/c (ellipsoid) = semi-axes.
How the Calculation Works
Step 1: Find the area of the base (a square, rectangle, circle or triangle).
Step 2: For prisms and cylinders, multiply the base area by the height. For cones and pyramids, which taper to a point, take one-third of that.
Step 3: Spheres, hemispheres and ellipsoids use their own formulas based on the radius or semi-axes.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| r | Radius | cm, m, in, ft |
| h | Vertical height | cm, m, in, ft |
| V | Volume | cm³, m³, L, mL, gal, in³, ft³, yd³ |
Example Calculation
Cylinder
Given: radius = 3 cm, height = 10 cm
Calculation: V = 3.14159 × 3² × 10
Result: V ≈ 282.74 cm³ (about 0.283 L)
Cone
Given: radius = 3 cm, height = 4 cm
Result: V = 3.14159 × 9 × 4 ÷ 3 ≈ 37.70 cm³
Ellipsoid
Given: semi-axes 5, 4 and 3 cm
Result: V = (4/3) × 3.14159 × 60 ≈ 251.33 cm³
Volume Conversion Table
| Unit | Equivalent |
|---|---|
| 1 L | 1,000 cm³ = 1,000 mL |
| 1 m³ | 1,000 L |
| 1 US gal | 3.785 L = 231 in³ |
| 1 ft³ | 1,728 in³ ≈ 7.48 US gal ≈ 28.32 L |
| 1 yd³ | 27 ft³ |
Shape Properties
The one-third rule
A cone holds exactly one third of the cylinder with the same base and height; a pyramid holds one third of the matching prism.
Spheres and hemispheres
A hemisphere is exactly half a sphere, so its volume is (2/3)πr³. An ellipsoid becomes a sphere when all three semi-axes are equal.
Dimensions Explained
Use the inside dimensions to find how much a container holds, and the outside dimensions for the space an object takes up. Use the radius, not the diameter, for round shapes.
Frequently Asked Questions
How do you calculate the volume of a shape?
For prisms and cylinders multiply the base area by the height; for cones and pyramids take one third of that; for spheres use (4/3)πr³.
How do you convert cubic centimeters to liters?
Divide by 1,000. You can also switch the result unit to liters.
How many gallons are in a cubic foot?
About 7.48 US gallons.
What is the volume of a cone?
V = πr²h ÷ 3.
How do I find the volume of an irregular object?
Split it into simple shapes and add their volumes, or measure the water it displaces.