Cone Volume Calculator
A cone holds exactly one-third of the matching cylinder. Enter the base radius and the vertical height, pick a unit, and get the volume with every step shown.
Example: with Base radius (r) 4 · Height (h) 9 · Units inches (in) → Cone volume: 150.80 in³.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outThe cone volume formula: V = ⅓πr²h
To find the volume of a cone, compute the base area, multiply by the height, and take one-third: V = ⅓πr²h. With the defaults — a funnel-shaped cone with a 4 in radius and 9 in height — that’s ⅓ × π × 4² × 9 = 48π ≈ 150.80 in³. The matching cylinder would hold 144π ≈ 452.39 in³, exactly three times as much.
Use the vertical height — the perpendicular distance from the base to the tip — not the slanted side. If a spec sheet gives you the slant length ℓ, recover the height with h = √(ℓ² − r²): a cone with r = 3 and ℓ = 5 has h = √(25 − 9) = 4. And if you measured the diameter, halve it before entering the radius.
How it’s calculated
Volume = ⅓ × π × r² × h with full double-precision π, where h is the perpendicular height. The base area row is πr². Conversions: 1 US gallon = 231 in³ exactly, 1 ft³ = 7.48052 gal (NIST Handbook 44), 1 liter = 1,000 cm³, 1 m³ = 1,000 L.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Using the slant length as the height — the formula needs the perpendicular height from base to apex.
- Entering the diameter instead of the radius, which inflates the result 4×.
- Forgetting the ⅓ — πr²h alone gives the cylinder’s volume, three times too much.
Frequently asked questions
How do I find the volume of a cone?
Square the radius, multiply by π and the height, then divide by 3. For r = 4 in and h = 9 in: ⅓ × π × 16 × 9 ≈ 150.80 in³.
What is the volume of a truncated cone?
A truncated cone (frustum) uses V = ⅓πh(R² + Rr + r²), where R and r are the two radii. With R = 6, r = 3, h = 8: ⅓ × π × 8 × (36 + 18 + 9) ≈ 527.79 cubic units.
Why is a cone one-third of a cylinder?
Slicing shows a cone’s cross-sections shrink with the square of the distance from the base, and integrating that taper leaves exactly one-third of πr²h. Euclid proved the same ratio geometrically.
Do I use slant height or vertical height?
Vertical (perpendicular) height. If you only know the slant length ℓ, use h = √(ℓ² − r²) first — for r = 3 and ℓ = 5, h = 4.