Example 1
- Radius: 5
- Height: 12
314.16
Cone r = 5, h = 12: 314.16, one third of cylinder 942.48.
Cone volume calculator
Give the radius of the base circle and the height from the center of that base to the tip. You get one third of a cylinder with the same circle and the same height. At r = 5 and h = 12 the result is 314.16, the same 100π.
V = ⅓πr²h. A cylinder is on the cylinder volume calculator. A pyramid is on the pyramid volume calculator.
Result
Radius r (cm) and Height h (cm). Volume shows up here.
How it works
Cone volume is one third of a cylinder with the same circle and the same height. V = ⅓πr²h multiplies base area by h and divides by three. The calculator uses π and exact 1/3, not 0.33. Height is the segment from the center of the base to the tip, straight down, not the slant along the side.
The first card example, r = 5 and h = 12, is 314.16. That cylinder would be 942.48, three times larger. The pair r = 10 and h = 3 also yields 314.16, because (1/3)π×100×3 is the same 100π. A wide short solid and a narrower taller one can share a number. At r = 1 and h = 3 you get 3.14, the same digits as circle area at r = 1, a different shape.
Type the base radius, the same r as on the cylinder page, then height in the same unit. Click Calculate. If you know diameter, divide by two. Diameter 10 means r = 5; typing 10 as r with h = 12 overstates volume by four because r is squared. A comma and a period are the same.
A pyramid also divides by three, but it takes a ready base area and no π unless you already folded a circle into that area. That path is on the pyramid volume page. A sphere at r = 5 is about 523.60 and does not use h. Circle area of the base, with no height, lives on the circle page.
Slant height along the side is longer than h and is not an input. If a worksheet only gives slant and r, find height first, then come back. Switching to inches relabels the result as in³ and does not convert a typed 5.
Mixing cm in r with inches in h breaks the scale. Both numbers in one unit. The formula does not need a textbook-skinny cone: a short r = 7 and h = 3 is as legal as a slim r = 2 and h = 10.
How to use
- Type the base radius, the same r as on the cylinder page, in cm or inches.
- Type height from the center of the base to the tip, straight down, in the same unit.
- Click Calculate. At r = 5 and h = 12 you get 314.16, one third of cylinder 942.48.
- If you know diameter, divide by two. Do not type diameter in the r field.
- Open a pyramid with a ready base area on its own page. Here the base is a circle, so πr².
Formula
V = (1/3) × π × r² × h
One third of a cylinder with the same r and h. Slant height is not the height input.
V of a cone r = 5, h = 12
One third of a cylinder with the same circle. At r = 5 and h = 12 the result is 314.16, the same 100π.
- V
- Volume (1/3)πr²h. 5 and 12 give 314.16, one third of cylinder 942.48. r = 3 and h = 9 is 84.82.
- r
- Radius of the base circle. 5 with h = 12 is 314.16. Slant height is not this field.
- h
- Height from the center of the base to the tip. 12 with r = 5. r = 1 and h = 3 give 3.14.
- π
- In the product with r² and h / 3. 100π at r = 5 and h = 12 is that 314.16.
Examples
Example 2
- Radius: 3
- Height: 9
84.82
A smaller cone r = 3, h = 9.
Example 3
- Radius: 1
- Height: 3
3.14
r = 1, h = 3. The 3.14 matches circle area at r = 1, different shape.
Example 4
- Radius: 10
- Height: 3
314.16
A wide short cone r = 10, h = 3. The same 314.16 as the first example.
Example 5
- Radius: 2
- Height: 10
41.89
Slim r = 2, h = 10.
Example 6
- Radius: 4
- Height: 6
100.53
r = 4, h = 6, a moderate height.
Example 7
- Radius: 6
- Height: 12
452.39
r = 6, h = 12, twice the r of the first example at the same h.
Example 8
- Radius: 7
- Height: 3
153.94
Short r = 7, h = 3.
Frequently asked questions
What does a cone with r = 5 and h = 12 give?
314.16, which is 100π. A cylinder with the same r and h is 942.48, three times larger.
How is a cone different from a cylinder?
A cylinder with the same r and h is three times larger. At 5 and 12 the cone is 314.16 and the cylinder is 942.48.
Why do 5 and 12 give 314.16, the same as circle area at r = 10?
Because (1/3)π×25×12 = 100π. Circle area at r = 10 is also 100π. Different shape, same number. A coincidence of the formulas.
Do I compute a pyramid here?
The base here is a circle, so πr². A pyramid takes a ready base area on its own page.
Is diameter 10 the same as r = 10?
Diameter 10 means r = 5. Typing 10 as r with h = 12 overstates volume by four.
Is height the slant length of the cone?
h drops perpendicular onto the base. The slant is longer and is not an input.
Is a sphere at r = 5 the same 314?
A sphere at r = 5 is about 523.60. A cone needs height. Different solid.
Is π 22/7 here?
The calculator uses π and exact 1/3. At r = 1 and h = 3 the display is 3.14 to two places.
Why a second example at 314.16?
The pair 10 and 3 shows another solid with the same 100π. Wide and short versus 5 and 12.
Can r be in cm and h in inches?
Both numbers in one unit, then cm³ or in³ from the switch. Mixing breaks the scale.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.