Cone volume calculator

Find cone volume from the base radius and perpendicular height. Apply V = πr²h ÷ 3 and check a worked example with a result in cubic units.

Result

One third of a cylinder

A cone and cylinder with matching base and height have volumes in a one-to-three ratio. The dashed cylinder makes this comparison visible.

How do you calculate cone volume?

Multiply base area by perpendicular height, then divide by three. Height runs from the tip to the base plane; it is different from slant height.

V = \frac{π \times r^{2} \times h}{3}

r = \frac{d}{2}

How to use the calculator

Enter measurements with a decimal point or comma: results update immediately. Input units apply to every length; changing them converts the measurements. Changing result units leaves the shape unchanged. The control below the drawing reveals or hides its visual explanation. Copy results includes valid measurements and the result. Reset and Try this example restore the initial values and centimetre units.

Choose radius or diameter: switching preserves the shape’s dimensions. Drawing handles always change the radius and also update the diameter when selected.

The first formula shows the relationship; the second substitutes measurements converted to the result unit. The ≈ sign indicates rounding, including in the substituted values.

A small cone

With radius 3 cm and height 6 cm, the matching cylinder holds 54π cm³. The cone takes one third: 18π cm³, approximately 56.55 cm³.

From measurements to the result

Input: $r = 3 cm; h = 6 cm$
Result: $≈ 56.55 {cm}^{3}$

Calculation steps

Multiply the radius squared by the height.
$r^{2} \times h = 9 \times 6 = 54$
Complete the calculation using the tool’s formula.
$V = \frac{54}{3} \times π = 18 \times π$

Units and interpretation

Volume uses cubic units: 1 m³ = 1,000,000 cm³ = 1,000 L. Capacity in litres is geometric; use internal measurements for real containers.

The drawing represents a right cone. Radius and height do not describe wall thickness or the material volume of a hollow cone.

Precision and numerical limits

Lengths range from 0 to 10¹² in the selected unit; triangle sides must be strictly positive. Results use two decimal places, with scientific notation for very small or large values. Calculations use browser precision: unrepresentable positive values produce an error. A rejected unit change keeps the previous data. Calculation takes place in your browser.

Maximum diameter is 10¹² in the input unit. A rejected mode change keeps the previous data.

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Cone volume calculator

Result

One third of a cylinder

How do you calculate cone volume?

How to use the calculator

A small cone

From measurements to the result

Calculation steps

Units and interpretation

You might also need

Circle area

Circle circumference

Triangle area