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Cone Radius from Volume Calculator.

Find a right circular cone's base radius from its volume and vertical height.

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radius: 3.09019362

radius

3.09019362

Results update automatically as you type.

Find a right circular cone's base radius from its volume and vertical height.

Use Cases

Design and Manufacturing

Determine the base radius of a conical component when you know its volume and height, useful for prototyping or quality control.

Example: A cone-shaped container has a volume of 500 cm³ and a height of 15 cm. Find its base radius.

Educational Problem Solving

Solve geometry homework or exam problems that ask for the radius of a cone given its volume and height.

Example: Given V = 100 in³ and h = 6 in, what is the radius?

Frequently Asked Questions

How do I find the radius of a cone from volume and height?
Use the formula r = sqrt(3V / (πh)), where V is the volume, h is the height, and π is approximately 3.14159. This calculator does that calculation for you.
What units should I use for volume and height?
You can use any consistent units, such as cubic inches for volume and inches for height, or cubic centimeters and centimeters. The radius will be in the same linear unit as the height.
Can I use this calculator for a cone with a slanted height?
No, this calculator requires the vertical height (perpendicular from base to apex), not the slanted height. Ensure you enter the vertical height for accurate results.

Tips & Common Mistakes

Tips

  • Ensure the volume and height are in compatible units (e.g., cubic inches with inches) to get the radius in the correct unit.
  • Double-check that you are entering the vertical height, not the slant height, as the formula uses vertical height.
  • If you have the diameter, remember to divide by 2 to get the radius, but this calculator directly gives the radius.
  • Use the transparent formula display to verify your manual calculations or understand the steps.

Common Mistakes to Avoid

  • Using the slant height instead of the vertical height, which leads to an incorrect radius.
  • Mixing units, such as entering volume in cubic feet and height in inches, without converting to a consistent system.
  • Forgetting to take the square root after computing 3V/(πh), resulting in the squared radius.

Last updated: August 13, 2026