Case 1
- Base radius
- 3
- Height
- 10
282.743339
Open with these valuesCylinder Volume Calculator
282.743339units³
Result: 282.743339 units³The base circle times the height: πr²h. That makes a cylinder exactly three times the cone with the same base and height. Enter the radius, not the diameter — a tin measured across at 10 has a radius of 5.
The numbers at a glance
Held fixed: Base radius 3.000.
| Height | Result |
|---|---|
| 2.500 | 70.685835 |
| 5.000 | 141.371669 |
| 7.500 | 212.057504 |
| 10.000Your value | 282.743339 |
| 12.500 | 353.429174 |
| 15.000 | 424.115008 |
| 17.500 | 494.800843 |
| 20.000 | 565.486678 |
Worked examples
Case 2
- Base radius
- 1
- Height
- 1
3.141593
Open with these valuesCase 3
- Base radius
- 5
- Height
- 2
157.079633
Open with these valuesHow it's calculated
V = π × r² × h
- StepMeasure the radius of the circular end.
- StepMeasure the height between the two ends.
- ResultRead the volume in the cube of the unit you entered.
What this number means
Centimetres in, cubic centimetres out
1000 cm³ make a litre. A tank of radius 30 cm and height 100 cm holds about 282 743 cm³, so roughly 283 litres.
The radius is squared, the height is not
Doubling the height doubles the volume; doubling the radius quadruples it. Radius 3 with height 10 gives 282.74, radius 6 with the same height gives 1130.97.
A tilted cylinder holds the same
Slanting the sides changes nothing, as long as the height is still measured perpendicular between the two ends.
Commonly misread
I measured in centimetres, so I can read the answer as litres.
The answer is cubic centimetres. Divide by 1000 for litres: 282 743 cm³ is about 283 litres.
I divided by three, the way the cone formula does.
The cylinder takes the full base circle times the height. The third belongs to the cone, which fits into it three times over.
Radius and height can be swapped, the product is the same.
Only the radius is squared. Swapping the two passes the check at radius 1 and height 1, then fails at radius 0.5 and height 4, where the volume is π.
Reference table
| Radius, height | Exact | Volume |
|---|---|---|
| 0.5, 4 | π | 3.141593 |
| 1, 1 | π | 3.141593 |
| 2, 7 | 28π | 87.964594 |
| 5, 2 | 50π | 157.079633 |
| 3, 10 | 90π | 282.743339 |
Questions
How do you calculate the volume of a cylinder?
Square the radius, multiply by π to get the base circle, then multiply by the height. Radius 3 and height 10 give 90π, about 282.74 cubic units.
How many litres does my tank hold?
Work in centimetres and the result is cubic centimetres, of which 1000 make a litre. A tank of radius 30 cm and height 100 cm holds about 282 743 cm³, so roughly 283 litres.
Why is a cylinder three times the cone?
Three cones with the same base and height fill it exactly. That is why the cone formula carries the one third and this one does not.
Does a tilted cylinder hold the same?
Yes, as long as the height is measured perpendicular between the two ends. Slanting the sides without changing that height leaves the volume unchanged.
Sources and last check
Information, not professional advice.