Geometry
Cylinder Volume Calculator
Find the volume of a cylinder from its radius, diameter, or circumference and height using V = πr²h. Mix units per field, read the answer in litres or gallons, and see the surface areas and every step — live as you type.
Cylinder dimensions
V = πr²hDescribe the round base by
Volume
1,178
Also equals
1.18
m³
41.6
ft³
311.2
gal (US)
Base area
0.7854 m²
Side area
4.71 m²
Total area
6.28 m²
Updates as you type.
Try a real object
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The basics
What is the volume of a cylinder?
A cylinder is a circle pushed straight up into a solid — think of a can, a pipe, or a water tank. Its volume is simply the area of that circular base multiplied by how tall it is. That single idea, base area times height, is all the formula encodes.
A = πr²
The circular base
Every slice of the cylinder is the same circle, of radius r. Its area is π times the radius squared — the part that makes a cylinder different from a box.
π × 5² ≈ 78.54 cm²
V = πr²h
Stacked through the height
Stack that base through a height of h and the area sweeps out a volume. Multiply the base area by the height and you have it.
78.54 × 20 ≈ 1,570.8 cm³
Method
How to calculate it by hand
Four short steps take you from a measurement to a volume in any unit you like.
- 1
Find the radius
If you measured the diameter, halve it (r = d ÷ 2). From a circumference, divide by 2π. Keep the radius and height in the same length unit.
r = d ÷ 2 - 2
Square the radius
Multiply the radius by itself. This is the r² that turns a length into the area factor of the base.
r × r = r² - 3
Multiply by π for the base area
Multiply r² by π (about 3.14159) to get the area of the circular base.
A = π × r² - 4
Multiply the base area by the height
That gives the volume. The answer is in cubic units of the length unit you used.
V = A × h = πr²h
Worked examples
See it on real objects
The same procedure handles a soda can, a water tank, and a length of pipe — only the numbers and units change.
A cylindrical tank 1 m across and 1.5 m tall — how many litres does it hold?
Given d = 1 m, h = 1.5 m
Radius: 1 ÷ 2 = 0.5 m
Base area πr²: π × (0.5 m)² = 0.7854 m²
Volume πr²h: 0.7854 × 1.5 = 1.18 m³
Volume = 1,178 L
Quick chart
How much does a round tank hold?
Common diameters and heights, worked out to capacity. Switch between metric (litres) and imperial (US gallons) for tanks, pools, and drums.
Capacity in L · diameter and height in m
| ⌀ \ height | 0.5 m | 1 m | 1.5 m | 2 m | 3 m |
|---|---|---|---|---|---|
| 0.5 m | 98.17 | 196.3 | 294.5 | 392.7 | 589 |
| 1 m | 392.7 | 785.4 | 1,178 | 1,571 | 2,356 |
| 1.5 m | 883.6 | 1,767 | 2,651 | 3,534 | 5,301 |
| 2 m | 1,571 | 3,142 | 4,712 | 6,283 | 9,425 |
| 2.5 m | 2,454 | 4,909 | 7,363 | 9,817 | 14,726 |
| 3 m | 3,534 | 7,069 | 10,603 | 14,137 | 21,206 |
Read a row (diameter) across to a column (height) for the capacity. Values use V = πr²h, then convert to L.
Where it shows up
Why cylinder volume matters
Round things are everywhere, so this one formula does a lot of quiet, practical work.
πr²h → litres
Tanks & pools
Sizing a water tank, fish tank, or round pool means turning its dimensions into a capacity in litres or gallons.
πr²L → flow
Pipes & ducts
The volume of a pipe sets how much water, air, or gas it holds and how fast a length fills or drains.
πr²h → fill
Cans & packaging
Cans, jars, and tubes are cylinders; their volume fixes the fill amount printed on the label.
Reference
The cylinder formula family
Volume is one of four quantities you can read off the same two measurements, radius and height.
V = πr²h
Volume
Base area times height. The headline number for capacity.
space inside — what it holds
A = 2πrh
Lateral (side) area
The curved side only — unroll it into a rectangle of width 2πr and height h.
the curved label area
A = 2πr²
Area of the two ends
The two circular caps together. Add these to the side for the full skin.
the top + bottom discs
A = 2πr(r + h)
Total surface area
Everything on the outside — the metal you would need to build it.
ends + side
Worth knowing
Rules and common mistakes
A few habits keep cylinder volume right every time.
r = d ÷ 2
Radius, not diameter
The single most common error: plugging the diameter into r. The formula needs the radius, so halve the diameter first.
r → r²
Square the radius, not the height
Only the radius is squared. The height enters to the first power — doubling the height doubles the volume, but doubling the radius quadruples it.
same unit
Match the units
Radius and height must be in the same length unit before multiplying. Mixing cm and m without converting is a classic slip.
units³
The answer is cubic
Volume is always in cubic units — cm³, m³, in³ — because three lengths are multiplied together. Surface area, by contrast, is square units.
V = πr²h
Solid vs. hollow
This is the volume of a solid cylinder. For a pipe wall, subtract the inner cylinder: π(R² − r²)h.
× 1000
m³ to litres
One cubic metre is exactly 1,000 litres. It is the conversion people forget most when sizing big tanks.
Related shapes
How it compares
The base-area-times-height idea connects the cylinder to its neighbours.
V = ⅓πr²h
Cone
A cone with the same base and height holds exactly one-third of the cylinder.
V = ⁴⁄₃πr³
Sphere
A sphere of radius r fills two-thirds of the smallest cylinder that contains it.
V = l × w × h
Rectangular prism
Swap the circular base for a rectangle and πr² becomes length × width — same recipe, different base.
Conversions
Volume unit cheat-sheet
Once you have a volume, these are the conversions you will reach for most.
| From | Equals |
|---|---|
| 1 m³ | 1,000 litres = 1,000,000 cm³ |
| 1 litre | 1,000 cm³ = 1,000 mL |
| 1 US gallon | 231 in³ ≈ 3.785 litres |
| 1 UK gallon | ≈ 4.546 litres |
| 1 ft³ | ≈ 28.32 litres ≈ 7.48 US gallons |
| 1 in³ | ≈ 16.39 cm³ ≈ 16.39 mL |
FAQ
Common questions
The volume of a cylinder is V = πr²h — the area of the circular base (πr²) times the height (h). Square the radius, multiply by π to get the base area, then multiply by the height.
The radius is half the diameter, so divide the diameter by 2 first, then use V = πr²h. For a diameter of 10 cm and height 20 cm, r = 5 cm, base area = π × 5² ≈ 78.54 cm², and the volume ≈ 1,570.8 cm³.
Work out the volume in cubic units first, then convert: 1 litre = 1,000 cm³, 1 cubic metre = 1,000 litres, 1 US gallon = 231 in³ ≈ 3.785 litres, and 1 cubic foot ≈ 7.48 US gallons. This calculator does the conversion for you — just pick the output unit.
Volume is in cubic units of whatever length unit you used: centimetres give cm³, inches give in³, metres give m³. Keep the radius and height in the same base unit, or let the calculator's per-field unit menus handle the conversion.
Yes. Each field has its own unit menu, so you can enter a pipe's diameter in inches and its length in feet. The calculator converts both to a common base before computing, which is exactly how you should do it by hand too.
Volume (πr²h) measures the space inside — how much it holds. Surface area measures the outside skin: the two circular ends (2πr²) plus the curved side (2πrh), giving total surface area 2πr(r + h). The calculator shows both.
Rearrange V = πr²h to h = V ÷ (πr²). Divide the known volume by the base area πr². For example, a volume of 500 cm³ with radius 5 cm gives h = 500 ÷ (π × 25) ≈ 6.37 cm.
Yes in principle — both are base area × height. A prism's base is a polygon (area = length × width for a box), while a cylinder's base is a circle (area = πr²). The 'stack the base through the height' idea is identical.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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