Geometry
Volume of a Cone Calculator
Find a cone's volume from its radius or diameter and its height or slant height. Switch units, see the capacity in litres and gallons, the surface area, and every step — all updating live as you type.
Cone dimensions
Volume (cm³)
37.6991
V = ⅓ · π · 3² · 4
Litres
0.038
US gallons
0.01
Slant height l
5 cm
Base area
28.2743 cm²
Lateral area
47.1239 cm²
Total surface
75.3982 cm²
Try a real cone
No sign-up · Free
The basics
What is the volume of a cone?
A cone is a solid with a circular base that narrows smoothly to a single point, the apex. Its volume is the amount of space it encloses. The whole calculation rests on two numbers — the radius of the base and the perpendicular height — and one tidy formula.
V = ⅓ · π · r² · h
The cone volume formula
The base area π·r² times the height h, all scaled by one-third. The r is the base radius and h is measured straight up from the centre of the base to the apex.
r = 3, h = 4 → V ≈ 37.699
cone = ⅓ × cylinder
One-third of a cylinder
Stand a cone inside a cylinder of the same base and height and it fills exactly a third of it. That is why the formula is the cylinder's π·r²·h with a ⅓ in front.
cylinder ≈ 113.10 → cone ≈ 37.70
Method
How to calculate it by hand
Four short steps take any radius and height to a volume — the same order the calculator follows.
- 1
Get the radius
You need the base radius r. If you measured the diameter, halve it. Make sure the radius and height share the same unit.
r = d ÷ 2 - 2
Square the radius
Multiply the radius by itself. This is the heart of the base area π·r².
r² = 3 × 3 = 9 - 3
Multiply by π and the height
Multiply the squared radius by π (≈ 3.14159) and by the height h. This is the volume of the surrounding cylinder.
π · 9 · 4 = 113.097 - 4
Take one-third
Divide by 3 (or multiply by ⅓). The result is the cone's volume, in cubic units.
113.097 ÷ 3 ≈ 37.699
Worked examples
See it on real cones
The same formula handles an ice cream cone, a traffic cone, a party hat — and even a frustum, a cone with its tip cut off.
Given r = 1.5 cm, h = 12 cm
Square the radius: r² = 2.25
Plug in: V = ⅓ · π · 2.25 · 12
Evaluate: ⅓ · 84.823
V = 28.2743 cm³
Quick chart
Volume of a cone for common sizes
A fast lookup for “what is the volume of a cone with radius X and height Y?” Read down to your radius, across to your height.
Volume in cubic units · rows = radius · columns = height
| r \ h | 2 | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|---|
| 1 | 2.1 | 4.2 | 6.3 | 8.4 | 10.5 | 12.6 |
| 2 | 8.4 | 16.8 | 25.1 | 33.5 | 41.9 | 50.3 |
| 3 | 18.8 | 37.7 | 56.5 | 75.4 | 94.2 | 113.1 |
| 4 | 33.5 | 67 | 100.5 | 134 | 167.6 | 201.1 |
| 5 | 52.4 | 104.7 | 157.1 | 209.4 | 261.8 | 314.2 |
| 6 | 75.4 | 150.8 | 226.2 | 301.6 | 377 | 452.4 |
| 7 | 102.6 | 205.3 | 307.9 | 410.5 | 513.1 | 615.8 |
| 8 | 134 | 268.1 | 402.1 | 536.2 | 670.2 | 804.2 |
| 9 | 169.6 | 339.3 | 508.9 | 678.6 | 848.2 | 1,017.9 |
| 10 | 209.4 | 418.9 | 628.3 | 837.8 | 1,047.2 | 1,256.6 |
Example: a cone with radius 3 and height 6 holds 56.55 cubic units.
Where it shows up
Why cone volume matters
One formula behind a surprising range of everyday volumes — from kitchens to construction sites.
grain & gravel
Stockpiles
A heap of sand, gravel or grain poured onto the ground forms a cone. Its volume tells a site how much material is in the pile without weighing it.
funnels & cups
Capacity
Funnels, paper cups and ice cream cones are cones. Volume tells you how much liquid or scoop they hold before they overflow.
roofs & spires
Construction
Conical roofs, silo tops and tipi tents use cone volume and surface area to estimate enclosed space and the material needed to cover them.
Related formulas
The cone formula family
Volume rarely travels alone. These companions cover the surface, the sloped side and the truncated cone.
l = √(r² + h²)
Slant height
The slant height is the straight-line distance up the sloped surface. It comes from the right triangle formed by the radius and the height — Pythagoras in disguise.
A = π · r · l
Lateral surface area
The curved surface (everything except the base) equals π times the radius times the slant height l.
A = π · r · (r + l)
Total surface area
Add the circular base π·r² to the lateral surface for the full skin of the cone.
V = ⅓ · π · h · (R² + Rr + r²)
Frustum (truncated cone)
Slice the tip off a cone and you get a frustum with two radii, R and r. Buckets and lampshades use this version.
Worth knowing
Rules and common mistakes
The arithmetic is short, so most errors are about which number goes where. Keep these in view.
h, not l
Use the perpendicular height
The formula needs the straight-up height to the apex, not the slant along the side. Using the slant by mistake overstates the volume. Convert with h = √(l² − r²) first.
r = d ÷ 2
Radius, not diameter
The formula squares the radius. Dropping the diameter in by mistake makes the answer four times too large, since the radius is halved before squaring.
same unit
Match your units
Radius and height must be in the same unit before you multiply. Mixing centimetres and metres silently breaks the result.
cubic units
The answer is cubic
Volume is a three-dimensional measure, so it always comes out in cubic units — cm³, m³, in³ — never plain or square units.
× 2 height = × 2 V
Height scales linearly
Double the height and the volume doubles. Height enters the formula just once, so it scales the volume in direct proportion.
× 2 radius = × 4 V
Radius scales as a square
Double the radius and the volume quadruples, because the radius is squared. Small changes in radius move the volume a lot.
Compare
Cone vs cylinder vs sphere
With the same radius and a matched height, the three classic round solids line up in neat ratios — a handy sanity check.
V = ⅓ · π · r² · h
Cone
The smallest of the three for a given base and height — it tapers to a point, so it holds just a third of the cylinder.
V = π · r² · h
Cylinder
The full barrel: straight sides, no taper. A cone of the same base and height is exactly one-third of it.
V = (4/3) · π · r³
Sphere
For a sphere of radius r and a cone of the same radius and height 2r, the sphere is twice the cone — Archimedes' classic result.
FAQ
Common questions
The volume of a cone is V = ⅓·π·r²·h, where r is the radius of the circular base and h is the perpendicular height from the base to the apex. It is exactly one-third of a cylinder with the same base and height.
Square the radius, multiply by π, multiply by the height, then divide by 3. For a cone with radius 3 and height 4: 3² = 9, then 9 × π × 4 = 113.097, divided by 3 ≈ 37.699 cubic units.
A cone and a cylinder with the same base radius and height share the same base area, but the cone tapers to a point. Adding up the shrinking circular cross-sections (an integral) shows the cone fills exactly one-third of the matching cylinder, which is where the factor ⅓ comes from.
Halve the diameter to get the radius, then use V = ⅓·π·r²·h. If the diameter is 10, the radius is 5, so V = ⅓·π·5²·h. The calculator above does this automatically when you switch the input to diameter.
The slant height l is the distance along the sloped side. First recover the perpendicular height with h = √(l² − r²), then apply V = ⅓·π·r²·h. The slant must be longer than the radius for a real cone. Switch the height input to slant and the calculator handles it.
Volume is always in cubic units. If the radius and height are in centimetres, the volume is in cubic centimetres (cm³); in inches, cubic inches (in³). Both length measurements must be in the same unit before you calculate.
A frustum is a cone with the tip sliced off, leaving two circular faces of radii R and r separated by height h. Its volume is V = ⅓·π·h·(R² + R·r + r²). Buckets, lampshades and plant pots are common frustums.
Convert the volume to cubic metres, then multiply by 1000. A cone measured in centimetres gives cm³; divide cm³ by 1000 to get litres directly. The calculator shows litres and US gallons alongside the cubic-unit answer.
Keep going
Related calculators
Keep reading
Further reading
Math
Slope-Intercept Form (y = mx + b): How to Find and Graph It
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This guide shows how to find the equation from a graph, two points, or a point and slope, graph it, and convert standard form.
Ugo Charles
Math
The Cylinder Volume Formula (V = πr²h): How It Works, With Examples
The volume of a cylinder is V = πr²h, where r is the radius of the circular base, h is the height, and π ≈ 3.14159. This guide shows why the formula works, walks through a full numerical example, and covers diameter inputs and unit conversions.
Ugo Charles
Math
The Distance Formula: How to Find the Distance Between Two Points
The distance between two points is d = √((x₂−x₁)² + (y₂−y₁)²). It comes straight from the Pythagorean theorem: the horizontal and vertical gaps between the points are the two legs of a right triangle, and the distance is the hypotenuse.
Ugo Charles
Written by
UC
Author
Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
Did this solve your problem?