Cone Calculator
Calculate volume, total surface area, lateral area and slant height of a right cone.
About Cone Calculator
A right circular cone has volume (1/3)πr²h — exactly one-third of the cylinder with the same base and height. The slant height l = √(r²+h²).
Formulas
Volume
V = (1/3)πr²h
- r
- Base radius
- h
- Height
Lateral Area
LA = πrl
- r
- Base radius
- l
- Slant height
Worked example
With the default values below, Cone Calculator returns Volume of 150.7964. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Base Radiusminimum 0 units
- 4 units
- Heightminimum 0 units
- 9 units
Results
- Volume
- 150.7964 cu units
- Total Surface Area
- 174.0299 sq units
- Lateral Area
- 123.7644 sq units
- Slant Height
- 9.8489 units
Step by step
- 1Slant height= 9.8489
- 2Volume= 150.7964
- 3Lateral area= 123.7644
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is cone volume exactly 1/3 of a cylinder?
This can be proven via calculus (integration of circular cross-sections) or Cavalieri's principle.
What if I only know slant height and radius?
Height = √(l² − r²). The slant height, radius and height form a right triangle.