Geometry

Cone Volume Calculator

Calculate cone volume, slant height, base area, and lateral surface area from radius or diameter and vertical height.

Dimension Input Mode

Cone Base Radius (r)

Cone Height (h)

Primary Output Volume Unit

Cone Geometry

V = ⅓πr²h • s = √(r² + h²)

Cone Calculation Results

Decimals:

Volume in M3Live Output

3.1416m3

Additional Computed Dimensions

Slant Height (s)

3.1623 m

Base Surface Area

3.1416 m²

Total Surface Area

13.0762 m²

Equivalent Standard Volume Units

Liters (L)

3,141.5927 l

Cubic Centimeters (cm³)

3,141,592.6536 cm3

Cubic Feet (ft³ / cu ft)

110.9443 ft3

Cubic Inches (in³)

191,711.7461 in3

Cubic Yards (yd³)

4.109 yd3

US Liquid Gallons (gal)

829.921 us_gal

Imperial Gallons (UK gal)

691.0538 imp_gal

Mathematical Formula & Step-by-Step Derivation

SI Normalized Math

General Formula:

V = ⅓ × π × r² × h = ⅓ × π × (d / 2)² × h

Live Calculation With Your Input Values:

11. Cone Volume Formula

Formula: V = ⅓ × π × r² × h

Substituted: V = ⅓ × π × (1 m)² × (3 m)

Step Result: V = 3.1416 m3

Normalized in SI: ⅓ × π × (1 m)² × (3 m) = 3.1416 m³

22. Slant Height

Formula: s = √(r² + h²)

Substituted: s = √(1² + 3²)

Step Result: s = 3.1623 m (3.1623 m)

33. Total Surface Area

Formula: A = πr(r + s)

Substituted: A = π × 1 × (1 + 3.1623)

Step Result: A = 13.0762 m²

How to Calculate the Volume of a Right Circular Cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex. The volume of a cone is exactly one-third the volume of a cylinder with the same base and height.

Measure the base radius (r) and the vertical height (h) from base to apex.
Square the radius (r²) and multiply by Pi (π) to get the base area: A_base = πr².
Multiply the base area by the vertical height (h).
Divide by 3: V = ⅓ × π × r² × h.
To find the slant height (s), use the Pythagorean theorem: s = √(r² + h²).