What Is Volume?
Volume is how much space a solid takes up, or how much a container holds. It's measured in cubic units: a box 1 foot long, wide and tall holds 1 cubic foot. Liquids are often measured in liters or gallons instead, and the calculator gives both.
- Volume: the space inside, in cubic units such as in³, ft³ or cm³.
- Capacity: the volume a container can hold, often in liters, gallons or cups.
- Surface area: the total area of the outside, in square units. It tells you how much paint, wrapping or material covers the shape.
Which calculator should I use?
- Volume Calculator: for the space inside a 3D shape, such as a tank, a box or a planter.
- Square Footage Calculator: for a flat area, such as a floor or a yard, and the material and cost to cover it.
How to Calculate Volume
For any shape with the same cross-section all the way through, such as a box, a cylinder or a prism, multiply the area of the end by the length:
A shape that narrows to a point, such as a cone or a pyramid, holds exactly a third of that:
- V: the volume, in the cube of the unit you measured in.
- Base area: the area of the flat end: π × r² for a circle, length × width for a rectangle.
- h: the height or length, measured straight across, not along a slope.
Here is the formula for every shape in the calculator. The letters match the drawing and the box labels:
| Shape | Volume | Surface Area |
|---|---|---|
| Cube | a³ | 6a² |
| Rectangular box | l × w × h | 2(lw + lh + wh) |
| Sphere | 4/3 × π × r³ | 4 × π × r² |
| Hemisphere | 2/3 × π × r³ | 3 × π × r² |
| Spherical cap | π × h² × (3R − h) ÷ 3 | 2πRh + πh(2R − h) |
| Ellipsoid | 4/3 × π × a × b × c | about 4π((aᵖbᵖ + aᵖcᵖ + bᵖcᵖ) ÷ 3)^(1/p), p = 1.6075 |
| Cylinder | π × r² × h | 2πr(r + h) |
| Tube | π × (R² − r²) × h | 2πh(R + r) + 2π(R² − r²) |
| Capsule | π × r² × h + 4/3 × π × r³ | 2πrh + 4πr² |
| Cone | π × r² × h ÷ 3 | πr(r + s), s = √(r² + h²) |
| Cone frustum | π × h × (R² + Rr + r²) ÷ 3 | π(R + r)s + πR² + πr² |
| Triangular prism | triangle area × L | 2 × triangle area + (a + b + c) × L |
| Pyramid | l × w × h ÷ 3 | base + the four sloping triangles |
| Truncated pyramid | h × (a² + ab + b²) ÷ 3 | a² + b² + four sloping sides |
Example
A cylinder with a radius of 3 inches and a height of 8 inches, about the size of a large can:
- Base area: π × 3² = 28.27 in²
- Volume: 28.27 × 8 = 226.19 in³
- In liters: 226.19 × 0.016387 = 3.71 L, or 0.98 US gallons
How to Use the Volume Calculator
"How much does a cylinder 3 inches across the middle and 8 inches tall hold, in liters and gallons?" This calculator answers that.
Let's enter the numbers for this example in each box. They are already filled in when the calculator opens, so you can follow along and then change any box to match your own shape.
- Shape: Choose Cylinder. There are 14 shapes, and the drawing changes to show what each size means. Each shape remembers the sizes you typed, so you can switch and come back.
- Length Unit: Choose Inches, the unit of every size you enter. Millimeters, centimeters, meters, feet and yards work too.
- Radius (r): Enter 3, which is half the width of the round end. Sizes must be more than 0 and less than 1 million.
- Height (h): Enter 8, which is the distance between the two round ends.
Some sizes can be 0, turning the shape into a simpler one: a tube with no hole, a frustum or truncated pyramid with a pointed top, or a capsule with no middle. A few sizes have to fit together: a tube's inner radius must be smaller than the outer one, a cap can't be taller than its ball, and each side of a triangle must be shorter than the other two together.
Calculate and Reset
Click Calculate to see your results. If a box has a problem, such as a size of 0 or an inner radius bigger than the outer one, a message pops up under that box instead. Changing the shape or the unit shows the new results at once. With the default numbers you get:
- Your Results: a short summary in words: 226.19 in³, which is 3.71 liters or 0.98 US gallons, the weight of that much water, and the surface area.
- Volume: the headline, 226.19 in³, in the cube of your length unit.
- Liters and US Gallons: 3.71 and 0.98, how much liquid the shape holds.
- Surface Area: 207.35 in², the area of the whole outside including both ends.
- Weight of Water: 3.71 kg (8.17 lb), what the shape would weigh filled with fresh water, not counting the container.
- Volume in Other Units: the same volume in 13 units, from cubic millimeters to oil barrels, including cups, fluid ounces and imperial gallons.
- Share Results: a link that opens this calculator with your shape and sizes filled in. Copy it, or share it on Facebook or X.
Click Reset to go back to the default cylinder in inches and put every shape's sizes back to their defaults. The formulas are for perfect shapes; a real container's walls take up some of the space, so measure the inside for capacity.