What This Calculator Calculates
Enter a cone's base radius and perpendicular height to calculate its volume, total surface area, lateral surface area, base area, and slant height. The calculator shows the governing formula and formatted calculation steps with the result.
The Governing Formulas
For a right circular cone, the calculator uses:
- Slant height:
l = sqrt(r^2 + h^2). - Base area:
A_base = pi * r^2. - Lateral surface area:
A_lateral = pi * r * l. - Total surface area:
A_total = A_base + A_lateral. - Volume:
V = (1/3) * pi * r^2 * h.
Inputs & Supported Units
- Base radius: distance from the center of the circular base to its edge.
- Height: perpendicular distance from the base to the apex.
- Length units: millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles - the same unit is used for both radius and height.
- Area unit: automatically the squared version of the length unit you choose; volume unit: automatically the cubed version.
- The default unit is meters. The calculation converts entered values to meters internally, then converts displayed results back to the selected unit.
- Enter a positive unsigned decimal number. Empty values, zero, negative values, exponent notation, plus signs, other unsupported numeric syntax, and values above
1e12are rejected.
How to Use the Cone Volume Calculator
- Enter values in Base radius and Height.
- Select a Unit. The same unit applies to both inputs.
- Click Calculate. If an input fails validation, read the error and correct it.
- Review the five result values and the Formula & steps list. Displayed values are formatted before they appear, rather than shown at unlimited precision.
- After a valid result appears, click Copy result to attempt to copy the plain-text output, or click Download result (.txt) to download it.
- If clipboard access fails, the interface displays "Could not copy - select and copy manually." Use the displayed result for a manual copy.
- Click Reset to clear both inputs, restore meters, hide errors, and hide the result section.
Assumptions and Limitations
The calculator assumes a perfect right circular cone: the apex is directly above the center of a circular base. It does not handle oblique cones or truncated cones (frustums), and it uses only the entered radius and perpendicular height. It does not account for real-world tolerances, material, or measurement error, and it is not a substitute for professional or certified calculations.
Calculation Scope and Data Handling
The cone calculation runs locally in your browser from the values you enter and the fixed geometry formulas. This description covers the calculator logic only.
Frequently Asked Questions
What is the formula for the volume of a cone?
The volume of a right circular cone is V = (1/3) * pi * r^2 * h, where r is the base radius and h is the perpendicular height.
What is the formula for the surface area of a cone?
Total surface area is A = pi * r * (r + l), where l is the slant height. This is the base area pi * r^2 plus the lateral surface area pi * r * l.
How is slant height calculated?
Slant height is found with the Pythagorean theorem: l = sqrt(r^2 + h^2), treating the radius, height, and slant height as the two legs and hypotenuse of a right triangle.
What units does this calculator support?
Millimeters, centimeters, meters, kilometers, inches, feet, yards, and miles. Areas are shown in the squared version and volume in the cubed version of the unit you choose.
Does this calculator work for oblique cones?
No. It assumes a right circular cone, where the apex sits directly above the center of a circular base. Oblique cones require a different geometric treatment.