How to use the cone volume calculator
Enter positive numbers in Base radius and Height, then choose one shared Unit. After you click Calculate, the result shows five measurements, the calculation steps, and text you can copy or download.
- Type a positive number in Base radius.
- Type the perpendicular height in Height.
- Select the length unit in Unit.
- Click Calculate to display the measurements and formula steps.
- Use Copy result or Download result (.txt) once the result appears.
- Click Reset to clear both inputs, select Meters (m), and hide the result.
How to calculate cone volume
The calculator assumes a right circular cone. In the formula, r is the base radius and h is the perpendicular height. Volume uses V = (1/3) * pi * r^2 * h. The same radius and height also produce slant height and the three surface-area values.
Base radius: 4
Height: 9
Unit: Meters (m)
Slant height: 9.848858 m
Volume: 150.796447 m^3
Total surface area: 174.02988 m^2Cone surface area and slant height
The result reports base area, lateral surface area, total surface area, and slant height alongside volume. It calculates slant height with l = sqrt(r^2 + h^2), base area with A_base = pi * r^2, and lateral area with A_lateral = pi * r * l. Total surface area is the sum of the base and lateral areas. The Formula & steps list shows the values used in each calculation.
Cone calculator units and input rules
Unit applies to both Base radius and Height. You can choose millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles. Area values use the squared unit, and volume uses the cubed unit. The default selection is Meters (m). The calculation converts the inputs to meters internally, then displays the result in the selected unit.
Each input must be greater than zero and no larger than 1e12. The calculator accepts whole numbers and decimal values with at least one digit after the decimal point. Empty values, zero, negative values, exponent notation, plus signs, and other unsupported syntax trigger an error. Editing either input or changing Unit hides the old result until you click Calculate again.
Using the calculated measurements
Use lateral surface area when the required measurement covers the curved side. Use total surface area when the base is included. The result keeps both values separate, along with base area, volume, and slant height.
The text area below the result contains the inputs, all five measurements, and the numbered steps. Copy result sends that text to the clipboard when copying succeeds. Download result (.txt) saves the same text as a plain-text file.
The calculation runs locally in the browser from the values entered. The calculator code makes no request that sends those values elsewhere.
Which math calculator should you use?
Use this page for a right circular cone when you have its radius and perpendicular height. The Circle Area Calculator handles a circle's area, radius, diameter, or circumference from one known measurement. The Cylinder Volume Calculator handles a cylinder's volume and surface areas from radius and height. For several solid measurements in one place, use the Geometry Calculator. The Math Calculators page also lists calculators for equations, fractions, sequences, matrices, vectors, and number theory.
Frequently asked questions
What is the cone volume formula?
Use V = (1/3) * pi * r^2 * h, where r is Base radius and h is the perpendicular Height.
How do I calculate cone surface area?
Add base area pi * r^2 to lateral surface area pi * r * l, with l = sqrt(r^2 + h^2). The calculator reports both parts and their total.
What does Unit change in the cone volume calculator?
Unit sets the length for both Base radius and Height. Area uses square units, and volume uses cubic units. The choices are mm, cm, m, km, in, ft, yd, and mi.
Can I use this calculator for an oblique cone?
No. This calculator assumes a right circular cone, with the apex directly above the center of the circular base. It also does not calculate truncated cones, also called frustums.