Cone Volume Calculator
The volume of a cone is V = (1/3) π r² h, and this cone volume calculator works it out the moment you enter a radius (or diameter) and a height. You'll get the answer at once in cubic inches or feet, liters, and gallons, plus the result in terms of pi, the slant height, and the surface area. It handles a full cone or a frustum (a cone with the top cut off), and it shows the formula and steps with every result.
- Cone or frustum
- Radius or diameter
- Slant height shown
- In terms of pi
- Surface area too
Last updated June 15, 2026 Method: V = (1/3)πr²h Reviewed by the Calcowa math team
Enter a positive radius and height to see the volume.
Show all units
V = (1/3)π × 3² × 4 = 37.7 in³
What is the volume of a cone?
The volume of a cone is the space it fills, found with V = (1/3) × π × r² × h, where r is the base radius and h is the vertical height. For a radius of 3 in and a height of 4 in, the cone volume is about 37.7 cubic inches.
A cone is one-third of the cylinder that shares its base and height, which is where the one-third comes from. That's true for any right circular cone, the everyday kind whose tip sits straight above the center of the base. Tip straight up, base below.
How do you calculate the volume of a cone?
To find the volume of a cone, square the radius, multiply by pi and the height, then take a third. Here's the full sequence:
- 1
Measure the radiusMeasure the base radius. If you only have the diameter, divide it by 2.
- 2
Square the radiusMultiply the radius by itself to get r squared.
- 3
Multiply by pi and heightMultiply r squared by pi and by the vertical height.
- 4
Take one thirdMultiply that by one-third to get the volume.
- 5
Convert the unitsConvert to liters, gallons, or cubic feet if that's what you need.
Volume of a cone with the slant height
The volume formula uses the vertical height, not the slant. If you measured the slant height l along the sloping side, find the vertical height first with h = √(l² - r²), then use V = (1/3)πr²h. It's the Pythagorean theorem, since the radius, height, and slant form a right triangle. This calculator works from the vertical height and shows the slant height in the result, so you'll see both.
Volume of a frustum (truncated cone)
A frustum, or truncated cone, is a cone with the pointed top sliced off, and it's shaped like a bucket or a paper cup. It has a bottom radius R and a smaller top radius r, and its volume is V = (1/3) × π × h × (R² + Rr + r²). Switch the calculator to Frustum, enter both radii and the height, and it'll work out the truncated cone volume for you.
Volume of a cone in terms of pi
For a math class you'll often need the volume in terms of pi, which means leaving π as a symbol. Work out (1/3)r²h and keep the pi: for r = 3 and h = 4 that's (1/3) × 9 × 4 = 12, so the volume is 12π cubic units. The result panel shows this in-terms-of-pi value next to the decimal.
Surface area and volume of a cone
A cone's got two measures that often come up together. The volume, V = (1/3)πr²h, is the space inside. The total surface area, A = πr(r + l), is the curved side plus the round base, where l is the slant height. This calculator shows the surface area and slant height from the same inputs, so you'll read the area and volume of a cone together. For the full breakdown, see the cone surface area calculator.
A cone volume example, step by step
Say you've got a cone with a radius of 6 cm and a height of 9 cm. Square the radius to get 36, multiply by pi and by the height of 9 for about 1,017.88, then take a third.
V = (1/3)π × 6² × 9 = 108π ≈ 339.29 cm³
about 0.34 liters
Enter a radius of 6 and a height of 9 in centimeters above, and you'll get the matching liters and gallons at once.
Units and accuracy
Calcowa shows the cone volume in liters, US and UK gallons, milliliters, fluid ounces, and cubic mm, cm, m, inches, feet, and yards at once, plus the answer in terms of pi. The results use the full value of pi, not a rounded 3.14, so they're accurate for engineering, school, and everyday work.
| Unit | Best for | Good to know |
|---|---|---|
| Cubic inches (in³) | Funnels, small cones, party hats | Default when you enter inches |
| Cubic feet (ft³) | Piles of sand, gravel, grain | 1 ft³ = 1,728 in³ |
| Liters (L) | Cups, funnels, everyday capacity | 1 L = 1,000 mL |
| US gallons (gal) | Tanks and hoppers | 1 US gallon = 3.785 L |
| In terms of pi (π) | Exact math answers | Leaves the result as a multiple of pi |
Frequently asked questions
Is the volume of a cone one third of a cylinder?
Yes. A cone and a cylinder that share the same base radius and height are linked: three cone-fulls fill the cylinder exactly. So the cone volume is (1/3)πr²h, which is one-third of the cylinder's πr²h.
The volume of a cone is V = (1/3) × π × r² × h, where r is the base radius and h is the height. For a radius of 3 in and a height of 4 in, that's about 37.7 cubic inches. A cone holds exactly one-third of the cylinder with the same base and height.
The volume needs the vertical height, not the slant. If you have the slant height l, find the height first with h = √(l² - r²), then use V = (1/3)πr²h. The calculator works from the vertical height, so convert the slant first.
A frustum is a cone with the top cut off, so it has a bottom radius R and a top radius r. Its volume is V = (1/3) × π × h × (R² + Rr + r²). Switch the calculator to Frustum and enter both radii to get it.
Rearrange the formula to h = 3V ÷ (πr²). Multiply the volume by 3, then divide by pi times the radius squared. That gives you the height of a cone in the same length unit.
A cone and a cylinder with the same base and height are related: it takes exactly three cone-fulls to fill the matching cylinder. That's why the cone formula is the cylinder's πr²h multiplied by one-third.
Work out the volume the usual way, then read the litres or gallons line. The calculator shows litres, US and UK gallons, and millilitres next to the cubic units, so you don't have to convert by hand.
The total surface area of a cone is A = πr(r + l), where l is the slant height. This calculator shows the surface area and slant height next to the volume, and our cone surface area tool covers it in full.
Related calculators
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Sphere volumeVolume of a sphere, ball, or hemisphere.
Need a cone volume fast?
Try the calculator above, or browse every shape in the geometry hub.