Last updated: October 2026
How to calculate the volume of a cone
Short answer: square the radius, multiply by the height and by π, then divide by 3. With radius 5 cm and height 10 cm: 25 × 10 × 3.14159 ÷ 3 ≈ 261.8 cm³.
- Find the radius. If you measured the diameter, halve it. Radius is half the width of the circular base.
- Square it. Multiply the radius by itself: r².
- Multiply by height and π. r² × h × 3.14159.
- Divide by 3. A cone is one-third of its enclosing cylinder — that's the final step.
Example: a traffic cone with radius 15 cm and height 75 cm → 15² × 75 × π ÷ 3 = 225 × 75 × π ÷ 3 ≈ 17,671 cm³ (about 17.7 liters).
The cone volume formula
Short answer: V = ⅓πr²h — one-third times π times radius squared times height. The radius must be the true radius: if you have the diameter, use r = d ÷ 2.
V = ⅓ × π × r² × h
s (slant height) = √(r² + h²)
Lateral area = π × r × s
Total area = π × r × s + π × r²
Radius vs diameter is the #1 mistake: the formula squares the radius, so entering the diameter instead makes the answer 4× too large. The toggle above lets you enter either — it converts automatically. Read the geometric background on Wikipedia's cone article.
Cone vs cylinder: why one-third?
Short answer: three identical cones exactly fill the cylinder that encloses them — pour water from three cones into the cylinder and it fills to the brim. That's where the ⅓ in the formula comes from.
This isn't a fudge factor: integrate the shrinking circular cross-sections from base to apex and the math gives exactly one-third. Practically, it means a cone-shaped hopper holds a third of what the same-sized cylindrical tank would.
Volume calculator: more shapes
Short answer: this page handles cones. For bulk materials in cubic yards — mulch, gravel, soil, concrete — use our cubic yard calculator. Sphere, cylinder and cube volume tools are next in our geometry series.
Volume questions come in two flavors: geometry homework (this page) and ordering materials (our cubic yard calculator, which also converts to tons, bags and cost). Bookmark this page — the geometry cluster is growing.
Frequently asked questions
What is the volume of a cone?
The volume of a cone is one-third of the volume of a cylinder with the same base and height: V = ⅓πr²h. For example, a cone with radius 5 cm and height 10 cm has a volume of about 261.8 cm³.
How do you find the volume of a cone?
Square the radius, multiply by the height and by π, then divide by 3. With radius 5 and height 10: 5² × 10 × π ÷ 3 ≈ 261.8. The calculator above does it instantly, including the diameter case.
What is the cone volume formula?
V = ⅓πr²h, where r is the radius of the circular base and h is the perpendicular height. The ⅓ appears because a cone fills exactly one-third of the cylinder that encloses it.
Is there a volume formula calculator for other shapes?
This page covers cones. For bulk materials measured in cubic yards (mulch, gravel, soil, concrete), use our cubic yard calculator. More geometry volume tools — sphere, cylinder, cube — are on the way.
What does “cone calculator volume” mean?
It's just a word-order variant of “cone volume calculator” — a tool that computes a cone's volume from its radius and height. You're in the right place.
What is a “volume for cone calculator”?
Another phrasing of the same thing: a calculator for the volume of a cone. Enter the radius (or diameter) and height above and it returns the volume plus slant height and surface areas.
Should I enter the radius or the diameter?
Either — the tool has a toggle. The formula needs the radius, so if you only know the diameter, divide it by 2 (or just switch the toggle and enter the diameter directly).
What is the slant height of a cone?
The slant height is the distance from the apex to the edge of the base along the cone's side: s = √(r² + h²). It's needed for the lateral surface area (πrs). The calculator shows it automatically.
Is my data private?
Completely. Every calculation runs locally in your browser with JavaScript — your numbers are never sent to a server, stored, or tracked.
