Circle Volume Calculator
A circle is flat, so strictly speaking it has no volume at all. When people search for circle volume they mean the solid built on a circle: a cylinder, like a tank, a pipe, a can, or a round post hole. That is exactly what this calculator computes, with the working shown so you can check every step.
Enter a radius and height, or switch to diameter mode if you measured straight across, pick one unit, and get the volume in cubic units plus the liquid capacity in US gallons and liters. A third mode runs the formula backwards and finds the missing height from a known volume.
Pre-filled with the worked example from this page: radius 4 inches, height 10 inches. Results stay hidden until you click Calculate.
Quick Answer
- Quick Answer
- How to use this circle volume calculator
- The formula behind circle volume: base area times height
- Worked example: a small water tank, step by step
- A flat circle has area, not volume: the mistake this page prevents
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use this circle volume calculator
Three steps cover every mode. Pick how you measured, enter the two numbers, and click Calculate.
If you only have a tape wrapped around the container, that measurement is the circumference, and the companion circumference to volume calculator starts from exactly that number instead.
The formula behind circle volume: base area times height
A cylinder is a circle pushed straight up, so its volume is the area of the circle multiplied by the height. The area of a circle is pi times the radius squared, which gives the full formula V = pi x r squared x h, the same derivation taught in circle formula references and geometry courses everywhere.
Two consequences of that formula catch people out. First, the radius is squared, so doubling the radius quadruples the volume while doubling the height only doubles it. A wider tank grows capacity far faster than a taller one. Second, every measurement must share one unit before the multiplication, because the result is a product of three lengths. The tool enforces this by taking a single unit selector for both inputs.
| Radius | Height | Base area | Volume | Capacity |
|---|---|---|---|---|
| 4 in | 10 in | 50.27 in squared | 502.65 in cubed | 2.18 gal |
| 5 cm | 10 cm | 78.54 cm squared | 785.40 cm cubed | 0.79 L |
| 2 ft | 3 ft | 12.57 ft squared | 37.70 ft cubed | 282.02 gal |
| 1 m | 2 m | 3.14 m squared | 6.28 m cubed | 6,283.19 L |
Every row of that table was produced by the same formula the calculator runs, so you can type any row in and land on the same numbers.
Worked example: a small water tank, step by step
Take a cylindrical tank with a radius of 4 inches and a height of 10 inches. Square the radius: 4 squared is 16. Multiply by pi: 16 times 3.14159 is 50.27, which is the area of the circular base in square inches. Multiply by the height: 50.27 times 10 is 502.65 cubic inches.
For anything you pour, the liquid line matters more than the cubic figure. The tool converts through cubic centimeters: 502.65 cubic inches is 8,236.94 cubic centimeters, and dividing by 3,785.41 gives 2.18 US gallons, while dividing by 1,000 gives 8.24 liters. Run the same tank in reverse: tell the tool the volume is 500 cubic inches with a 4 inch radius, and it returns a fill height of 9.95 inches, just under the rim, which is the kind of check that stops an overflow before it happens.
A flat circle has area, not volume: the mistake this page prevents
The most common error in this topic is stopping halfway. Someone computes pi times r squared, gets 50.27, and reports it as the volume. That number is an area, in square units, and it describes only the footprint of the container. Volume needs the third dimension, the height, and the answer comes out in cubic units.
That is why the results box prints the base area on its own line, labeled as an area. If your shape is not a straight-sided cylinder at all, the neighbors differ: a ball uses the ball volume calculator with its cubed radius, a capsule-shaped tank uses the capsule volume calculator, and a plain rectangular pour belongs with the concrete volume calculator.
What competing calculators miss
Most pages ranking for this keyword accept a radius and a height and nothing else. They offer no unit selector, so an inch measurement read as centimeters quietly wrecks the answer. None of the top results convert the result into gallons or liters, even though capacity is the reason most people run this calculation. None accept a diameter, even though diameter is what a tape measure actually gives you across a round object, and none run the formula backwards to find a missing height. This page does all four, prints the base area separately to prevent the area-as-volume mistake, and shows its working in the results box.
Frequently Asked Questions
A circle on its own has no volume, because it is flat. The phrase means the volume of a cylinder with a circular base: V = pi x r squared x h. That is what this calculator computes, and it shows the base area separately so you can see where the flat circle ends and the solid begins.
Either one. Diameter mode halves your measurement for you, which suits a tape measure reading straight across a tank or can. Entering a diameter into the radius field by mistake makes the answer four times too big, because the radius is squared in the formula.
Use the third mode, Find height from volume. It rearranges the same formula: h = V divided by (pi x r squared). A 500 cubic inch container with a 4 inch radius needs 500 divided by 50.27, which is 9.95 inches of height.
It converts the volume to cubic centimeters first, then divides by 3,785.41 for US gallons and by 1,000 for liters. The worked example, 502.65 cubic inches, is 8,236.94 cubic centimeters, which gives 2.18 gallons and 8.24 liters.
The formula multiplies them together, so mixing inches for one and feet for the other silently produces a nonsense number. This tool takes a single unit for both measurements and converts internally, which removes that error entirely.
A cylinder has straight sides and two flat circular ends, so its volume is base area times height. A sphere uses V = (4/3) x pi x r cubed, and a cone holds exactly one third of the cylinder that shares its base and height.
Yes. Any shape with a circular cross-section and straight sides is this formula: a bored hole, a concrete footing form, a rain barrel, a fish tank, or a silo. Work in feet if you want the answer in cubic feet for ordering material.
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References
- Khan Academy, "Volume of a cylinder": the standard derivation of V = pi x r squared x h with worked examples. Khan Academy: Cylinder volume review. Accessed October 2026.
- National Institute of Standards and Technology, "Guide for the Use of the International System of Units": the unit conversion factors (1 inch = 2.54 cm exactly, 1 US gallon = 231 cubic inches) used for the capacity line. NIST: SI Units. Accessed October 2026.
- USGS Water Science School, "Water Density and Volume Conversions": 1 US gallon = 3.78541 liters, the conversion behind the gallons and liters output. USGS: Water Science School. Accessed October 2026.
- CK-12 Foundation, "Volume of Cylinders": an open textbook treatment of base area times height with practice problems matching the method used here. CK-12: Volume of Cylinders. Accessed October 2026.
- Math Open Reference, "Volume of a Cylinder": an interactive derivation showing why the radius is squared and the height is not. Math Open Reference: Cylinder Volume. Accessed October 2026.