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Cone Calculator: Volume, Slant Height and Surface Area

This free cone calculator finds the slant height, volume, lateral area and total surface area of a right circular cone from its radius and height. It shows the formulas.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

A cone narrows from a round base to a point. Funnels, party hats, ice cream cones and traffic cones are cones, and each needs its volume or the material for its side.

Enter the base radius and the height.

How to Use This Tool

  1. Enter the value or values asked for in the boxes.
  2. Choose the unit label if there is a choice.
  3. Press Calculate.
  4. Read every result in the table and copy what you need.

How the Calculation Works

The slant height is found with Pythagoras: l = √(r² + h²). Volume = ⅓πr²h. The side unrolls to a sector, so lateral area = πrl. The total adds the base: πr² + πrl.

Worked Example

A cone with radius 3 and height 4 has a slant height of 5, a volume of 37.6991, a lateral area of 47.1239 and a total surface area of 75.3982.

Common Uses

  • Funnels and hoppers.
  • Hats and costumes.
  • Piles of sand or grain.
  • Maths homework.

Tips and Common Mistakes

  • Use the vertical height, not the slant.
  • The same unit must be used for r and h.
  • Divide volume by 1,000 for litres if sizes are in cm.
  • Measure carefully: a small error in a length is squared in an area and cubed in a volume, so a 5 percent error in a side can become a 10 percent error in the area or a 15 percent error in the volume.
  • Round only at the end. If you copy a result into another calculation, copy the full number from the tool rather than a rounded one, so small errors do not build up.

Next, you may need the cylinder calculator, pyramid calculator, sphere calculator, circle calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Volume = ⅓πr²h, slant height = √(r² + h²), lateral area = πr × slant height and total surface area = πr(r + slant height).
The distance from the tip down the side to the edge of the base.
A cone with the same base and height as a cylinder holds exactly one third as much.
Yes. The tip sits straight above the centre of the base.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.