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Height of Cone Calculator.

Calculate cone height from volume and base radius.

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Set your values

Results update as you type.

Result: height: 10.610330 · volume: 100.000000

Result

height: 10.610330 · volume: 100.000000

Use Cases

Solve geometry homework problems

Quickly find the missing height of a cone when given its volume and base radius, a common problem in math classes.

Example: Find the height of a cone with volume 100 units³ and radius 5 units.

Check your manual calculations

Verify the height you computed by hand for a cone, ensuring accuracy for projects or assignments.

Example: Double-check a cone height calculation for a 3D modeling project.

Frequently Asked Questions

How do I calculate the height of a cone?
Use the formula h = (3 * Volume) / (π * r²), where Volume is the cone's volume and r is the base radius. Enter your volume and radius in the calculator to get the height instantly.
What units should I use for volume and radius?
The calculator accepts any consistent units. If you enter volume in cubic units and radius in the same linear units, the height will be in those linear units. For example, if volume is in cubic meters and radius in meters, height is in meters.
Can I use this calculator for a cone with a slanted height?
No, this calculator specifically computes the perpendicular height from the apex to the base center, using volume and base radius. It does not use slanted height or surface area.

Tips & Common Mistakes

Tips

  • Ensure your volume and radius are in consistent units (e.g., both in metric or both in imperial) to get the correct height unit.
  • If you have the diameter instead of the radius, divide the diameter by 2 to get the radius before entering it.
  • Remember that the height is the perpendicular distance from the base to the apex, not the slant height.
  • Use the formula h = (3 * Volume) / (π * r²) if you want to verify the calculator's result manually.

Common Mistakes to Avoid

  • Forgetting to multiply the volume by 3 before dividing by πr², which leads to a height that is one-third of the correct value.
  • Using the diameter instead of the radius in the formula, which gives a height that is four times too large.
  • Mixing units, such as entering volume in cubic inches and radius in centimeters, resulting in an incorrect height unit.

Last updated: August 13, 2026