Cylinder Volume Calculator

Calculate cylinder volume from radius or diameter and height. Convert measurement units, follow the calculation steps, and check base area and surface area.

Calculate Your Cylinder

Enter radius or diameter, then the perpendicular height. This tool uses a solid right circular cylinder.

Enter either radius or diameter; the other updates automatically. Diameter is twice the radius.

Distance between the circular bases, perpendicular to them. Each measurement can use a different unit.

Cylinder radius and height A cylinder with a radius marked on its top circular base and a perpendicular height marked beside its wall. r h
The circular bases appear as ellipses in this perspective. Diagram is not to scale.

Changing an input unit converts its measurement and preserves the cylinder size. Result units control the displayed outputs.

Need only the area of a circular base? Use the circle area calculator .

QUICK START

How to Use the Cylinder Volume Calculator

Start with a circular base measurement and the cylinder’s height, then follow the working to understand its volume.

  1. Enter radius or diameter

    Select the measurement’s unit, then fill either field. The other updates automatically because diameter = 2 × radius. Editing either field changes the cylinder’s base size.

  2. Add the perpendicular height

    Enter the distance between the circular bases. Height has its own unit selector, so it can use a different unit from the radius or diameter. All entered lengths must be positive.

  3. Choose result units and rounding

    Select the output unit and two, four or six decimal places. Volume appears in cubic units, such as cm³. Base area and surface area appear in squared units, such as cm².

  4. Review the calculation and copy

    Follow V = πr²h in the result panel. Check the supporting areas, then select Copy Result. Use Try an Example to load sample measurements or Clear to start again.

Calculating a container’s capacity? Use its internal radius or diameter and internal height for a cylindrical interior. External measurements include the container walls. For a concrete column or similar pour, the concrete calculator can help estimate concrete quantities.

WORKED EXAMPLES

Cylinder Volume Step by Step

Find the circular base area first, then multiply by the perpendicular height. If you know the diameter, divide it by two before using the radius formula.

EXAMPLE 01 · USING RADIUS

Calculate volume from radius and height

A cylinder has a radius of 3 cm and a height of 8 cm. Find its volume.

GIVEN MEASUREMENTS
Radius (r)
3 cm
Height (h)
8 cm
Diameter (d)
6 cm
  1. Calculate the circular base area

    A = πr² = π × 3² = 9π cm²

  2. Multiply by the height

    V = A × h = 9π × 8

    V = 72π cm³

  3. Round the decimal result

    72π ≈ 226.1947

ANSWER Volume ≈ 226.1947 cm³

The exact answer is 72π cm³. The decimal answer is rounded to four places.

EXAMPLE 02 · USING DIAMETER

Calculate volume from diameter and height

A cylinder has a diameter of 10 cm and a height of 20 cm. Find its volume.

GIVEN MEASUREMENTS
Diameter (d)
10 cm
Height (h)
20 cm
Radius (r = d ÷ 2)
5 cm
  1. Find the radius

    r = d ÷ 2 = 10 ÷ 2 = 5 cm

  2. Substitute into the volume formula

    V = πr²h = π × 5² × 20

    V = π × 25 × 20 = 500π cm³

  3. Round the decimal result

    500π ≈ 1,570.7963

ANSWER Volume ≈ 1,570.7963 cm³

You can also calculate directly from diameter: V = πd²h ÷ 4.

Check radius, units and rounding

Use the radius in V = πr²h and express all lengths in the same unit before calculating manually. Using the diameter as the radius makes the volume four times too large. Keep π until the final step, then check your measurements in the calculator .

FORMULA REFERENCE

Cylinder Formulas at a Glance

Use volume for the space inside a cylinder and surface area for its outer faces. These formulas describe a right circular cylinder.

Cylinder showing circular base area and height A = πr² h
Volume: V = πr²h Circular base area × height · cubic units
Cylinder net with two circles and one rectangle πr² 2πrh πr²
Surface area: S = 2πr² + 2πrh Two circular ends + curved wall · squared units
r = radius, d = diameter and h = perpendicular height. Use the same length unit throughout each calculation. Diagrams are not to scale.
Find Formula Result units
Radius from diameter r = d ÷ 2 Length, such as cm
Area of one base A = πr² Squared, such as cm²
Volume from radius V = πr²h Cubic, such as cm³
Volume from diameter V = πd²h ÷ 4 Cubic, such as cm³
Lateral surface area 2πrh Squared, such as cm²
Total surface area S = 2πr² + 2πrh Squared, such as cm²

Why does the diameter formula divide by four?

Radius is half the diameter. Substituting r = d ÷ 2 into V = πr²h gives V = π(d ÷ 2)²h. Since 2² = 4, this becomes πd²h ÷ 4.

How does the curved wall become a rectangle?

Unrolling a right cylinder’s wall gives a rectangle with width 2πr and height h. Its area is 2πrh. Adding both circular ends gives the total surface area. Explore Math Is Fun’s cylinder volume and surface area explanation for illustrated examples.

Ready to apply the formulas? Enter your cylinder measurements to see the working and results in your selected units.

CYLINDER CALCULATION GUIDANCE

Frequently Asked Questions

Find answers about cylinder dimensions, capacity, surface area and unit conversion.

How do I calculate cylinder volume from diameter?

Divide the diameter by two to find the radius, then use V = πr²h. Alternatively, use V = πd²h ÷ 4. For diameter 10 cm and height 20 cm, the volume is 500π cm³, or approximately 1,570.7963 cm³.

Do I need to enter both radius and diameter?

No. Enter either measurement and the other updates automatically. Your latest edit determines the circular base size. You also need to enter the cylinder’s perpendicular height to calculate volume.

Can radius and height use different units?

Yes. Each measurement has its own unit selector. For example, you can enter radius in centimeters and height in meters. The calculator converts the dimensions to your selected result unit before calculating. Changing an input unit converts its measurement while preserving the cylinder size.

How do I convert the cylinder volume to liters?

Divide a result in cm³ by 1,000, or multiply a result in m³ by 1,000, to obtain liters. 1 L = 1,000 cm³ = 0.001 m³. For example, 1,570.7963 cm³ is approximately 1.5708 L. The calculator displays cubic units; convert to liters separately. For volume-unit definitions, see the BIPM’s International System of Units brochure .

Should I use internal or external tank measurements?

Use the internal radius or diameter and internal height for a container with a cylindrical interior. External measurements include its walls. The calculated volume is the geometric capacity; usable capacity may be lower because of fittings, rounded ends or space left at the top.

Can this calculator find the volume of a hollow pipe?

The tool calculates a solid cylinder. To find the material volume of a hollow pipe, calculate the outer cylinder volume and subtract the inner cylinder volume: V = π(R² − r²)h. R is the outer radius and r is the inner radius. Use the same length and consistent units for both calculations.

Can I calculate a partly filled cylinder?

For an upright cylinder with a flat bottom, use its internal radius and the liquid depth as the height. A partly filled horizontal cylinder needs a circular-segment calculation, which this tool does not provide.

Does total surface area include the top and bottom?

Yes. Total surface area includes both circular ends and the curved wall: 2πr² + 2πrh. Lateral area includes only the curved wall. For a cylinder open at one end, its geometric surface area is πr² + 2πrh.

READY TO CALCULATE?

Find Your Cylinder’s Volume

Enter a radius or diameter and height, choose your result units, and follow the calculation. Copy the volume and supporting measurements when you’re ready.

Use Cylinder Volume Calculator