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.

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.

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.

Full original guide (expanded)

CalcDomain

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted text)

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 \(\displaystyle \alpha=\arctan\!\left(\frac{r}{h}\right)\).

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST DLMF (accessed Oct 25, 2025) — dlmf.nist.gov · Accessed 2026-01-19
https://dlmf.nist.gov/
Home — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/
Math — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/math
Geometry — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/geometry
Cylinder Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/cylinder-calculator
Sphere Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/sphere-calculator
Pyramid Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/pyramid-calculator

Changelog

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

0.1.0-draft · 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 on 2026-01-19
Profile · LinkedIn

, '

CalcDomain

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted text)

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 \(\displaystyle \alpha=\arctan\!\left(\frac{r}{h}\right)\).

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST DLMF (accessed Oct 25, 2025) — dlmf.nist.gov · Accessed 2026-01-19
https://dlmf.nist.gov/
Home — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/
Math — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/math
Geometry — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/geometry
Cylinder Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/cylinder-calculator
Sphere Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/sphere-calculator
Pyramid Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/pyramid-calculator

Changelog

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

0.1.0-draft · 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 on 2026-01-19
Profile · LinkedIn

]], displayMath: [['\\[','\\]']] }, svg: { fontCache: 'global' } };

CalcDomain

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted text)

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 \(\displaystyle \alpha=\arctan\!\left(\frac{r}{h}\right)\).

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST DLMF (accessed Oct 25, 2025) — dlmf.nist.gov · Accessed 2026-01-19
https://dlmf.nist.gov/
Home — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/
Math — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/math
Geometry — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/geometry
Cylinder Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/cylinder-calculator
Sphere Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/sphere-calculator
Pyramid Calculator — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/pyramid-calculator

Changelog

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

0.1.0-draft · 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 on 2026-01-19
Profile · LinkedIn

Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft

Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog

0.1.0-draft — 2026-01-19: Initial draft (review required).