Case 1
- Base radius
- 3
- Vertical height
- 4
37.699112
Open with these valuesCone Volume Calculator
Change any value to update the result.
37.699112units³
Volume: 37.699112 units³Examples
A cone holds exactly one third of the cylinder with the same base and height. Enter the radius and the vertical height in one length unit; the volume comes back cubed in that same unit. The slanted side is not needed here — that is the surface-area calculator.
The numbers at a glance
Held fixed: Base radius 3.000.
| Vertical height | Volume |
|---|---|
| 1.000 | 9.424778 |
| 2.000 | 18.849556 |
| 3.000 | 28.274334 |
| 4.000Your value | 37.699112 |
| 5.000 | 47.123890 |
| 6.000 | 56.548668 |
| 7.000 | 65.973446 |
| 8.000 | 75.398224 |
Worked examples
Case 2
- Base radius
- 1
- Vertical height
- 1
1.047198
Open with these valuesCase 3
- Base radius
- 5
- Vertical height
- 10
261.799388
Open with these valuesHow it's calculated
V = ⅓ × π × r² × h
- StepMeasure the radius of the circular base, not its diameter.Base radius=3
- StepMeasure the height straight up from the base to the tip.Vertical height=4·Base radius=3
- ResultRead the volume in the cube of the unit you entered.37.699112units³
What this number means
The height is not the slanted side
Measure straight up from the centre of the base to the tip. The slanted side is longer, so entering it in place of the height overstates the volume.
Exactly one third of the surrounding cylinder
Three identical cones fill the cylinder that shares their base and height. That ratio is a theorem of solid geometry, not an approximation.
Each row has a closed form beside it
Radius 3 with height 4 is 12π, written out as 37.699112. The table gives the exact multiple of π for every row, so nothing here has to be taken on trust.
Commonly misread
MisconceptionI measured along the sloping side, so that is my height.
CorrectionThat is the slant, and it belongs to the surface-area formula. The height runs from the centre of the base straight up to the tip.
MisconceptionA cone holds half of the cylinder with the same base and height.
CorrectionOne third. Three cones fill that cylinder exactly, which is where the ⅓ in the formula comes from.
MisconceptionRadius in centimetres, height in inches.
CorrectionBoth inputs have to use the same unit, and the answer then comes back in that unit cubed. Mixing two units gives a figure that means nothing.
Reference table
| Radius, height | Exact | Volume |
|---|---|---|
| 1, 1 | π ÷ 3 | 1.047198 |
| 0.5, 3 | π ÷ 4 | 0.785398 |
| 2, 6 | 8π | 25.132741 |
| 3, 4 | 12π | 37.699112 |
| 5, 10 | 250π ÷ 3 | 261.799388 |
Questions
How do you calculate the volume of a cone?
One third of π times the radius squared times the height. A cone with radius 3 and height 4 holds 12π, about 37.7 cubic units.
Why one third?
Three identical cones fill the cylinder that shares their base and height exactly. That ratio is a theorem of solid geometry, not an approximation.
Do I use the height or the slanted side?
The vertical height, measured straight up from the centre of the base to the tip. The slanted side is longer and belongs to the surface-area formula.
Which units does the answer use?
Whatever you entered, cubed. Radius and height in centimetres give cubic centimetres; in inches, cubic inches. Both inputs must use the same unit.