What inputs do I need to calculate a cone?

You can compute a cone from different pairs of values: radius and height, diameter and height, radius and slant height, or volume and height. The calculator lets you pick the pair you have.

What is the difference between lateral and total surface area?

Lateral surface area excludes the base and equals π·r·l. Total surface area includes the base: π·r·(r + l).

How do I find the apex (aperture) angle?

The full apex angle is 2·arctan(r/h). The half-angle at the axis is arctan(r/h).

Can I enter diameter instead of radius?

Yes. Choose the input mode “Diameter + Height” and the tool will convert diameter to radius automatically (r = d/2).

Which units does the calculator support?

Select Metric (mm, cm, m) or US/Imperial (in, ft). All results are shown coherently in the chosen unit system.

Does this calculator include frustums?

This page focuses on right circular cones. A frustum calculator is available separately and covers truncated cones.

Are the formulas valid for any cone?

Formulas here assume a right circular cone (axis perpendicular to base center). Oblique cones require integral methods and are outside this scope.

Cone Calculator — Volume, Surface Area, Slant Height & Angles

Professional cone calculator: compute volume, lateral and total surface area, slant height, base radius/diameter, and apex angle from your choice of inputs. Mobile-first, accessible, and accurate.

Measurement system

Metric mode defaults to centimeters and meters for length inputs.

Length unit

All outputs honor this single selection.

Known variables

Radius

Height

Volume (display unit cubed)

—

All other metrics derive from the same conversion-safe model.

Radius —

Height —

Diameter —

Slant —

Base area —

Lateral area —

Total area —

Volume —

Apex angle —

How to Use This Calculator

Pick the measurement mode that matches the values you have, select the length unit to keep things consistent, enter the known pair of quantities, and press Calculate. Inline guidance will flag invalid entries and the banner will summarize any remaining issues.

Methodology

The tool converts every input to meters (and cubic meters for volume) before applying the right-circular cone formulas. After computing radius, height, slant height, areas, volume, and apex angle in SI units, the results are converted back to the chosen display unit with a deterministic rounding strategy to avoid NaN/Infinity artifacts.

The apex angle reports the full opening across the base, while the half-angle happens to be half of that. Slant inputs are vetted so they must always exceed the radius to describe a real cone.

Full original guide (expanded)

Why use this calculator

Solve from multiple input pairs (r+h, d+h, r+l, V+h).
Clear formulas and variable glossary for transparency.
WCAG 2.1 AA compliant UI and mobile-first layout.

Related geometry tools

Frustum (Truncated Cone) Calculator (see dedicated tool).
Cylinder Calculator
Sphere Calculator
Pyramid Calculator

Audit & verification

Audit: Complete. Verified by Ugo Candido on 2026-01-19. Calculations match the original JavaScript engine and reference right circular cone formulas.

Code-generated audit notes are preserved so you can trace sources and version history.

Formulas

For a right circular cone with base radius \(r\), height \(h\), and slant height \(l=\sqrt{r^2+h^2}\): Base area: \(\displaystyle A_B=\pi r^2\) Lateral area: \(\displaystyle A_L=\pi r\,l\) Total area: \(\displaystyle A_T=\pi r(r+l)\) Volume: \(\displaystyle V=\frac{1}{3}\pi r^2 h\) Apex angle (full): \(\displaystyle \Theta = 2\,\arctan\!\left(\frac{r}{h}\right)\), half-angle \(\displaystyle \alpha=\arctan\!\left(\frac{r}{h}\right)\).

Citations

NIST DLMF (accessed Oct 25, 2025) — https://dlmf.nist.gov/ · Accessed 2026-01-19

Home — https://calcdomain.com/ · Accessed 2026-01-19

Math — https://calcdomain.com/math · Accessed 2026-01-19

Geometry — https://calcdomain.com/subcategories/geometry · Accessed 2026-01-19

Cylinder Calculator — https://calcdomain.com/cylinder-calculator · Accessed 2026-01-19

Sphere Calculator — https://calcdomain.com/sphere-calculator · Accessed 2026-01-19

Pyramid Calculator — https://calcdomain.com/pyramid-calculator · Accessed 2026-01-19

Changelog

Version: 0.1.0-draft · Last code update: 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

✓ Verified by Ugo Candido Last Updated: 2026-01-19 Version 0.1.0-draft

Version 1.5.0