Cone Volume Calculator

One formula. Two cone types. Instant results.

The cone volume calculator calculates volume for both standard right/oblique cones and truncated cones — enter your dimensions and get the exact volume in cubic centimeters without manual formula work.

What Is the Volume of a Cone?

The volume of a cone is the total three-dimensional space enclosed within its circular base and pointed apex — measuring exactly one-third the volume of a cylinder with the same radius and height.

Key components:

• r (Radius) — distance from the center of the base to its edge

• h (Height) — perpendicular distance from apex to the center of the base

• π — approximately 3.14159

• Units — cubic units (cm³, m³, in³)

Cone Volume Equation

Standard Formula (Right/Oblique Cone)

V = ⅓ × π × r² × h

Or equivalently:

V = ⅓ × Base Area × Height

Alternative Formula Using Diameter

Since radius = diameter ÷ 2:

V = (1/12) × π × d² × h

Alternative Formula Using Slant Height

If slant height (l) and radius (r) are known, find height first:

h = √(l² − r²)

Then apply the standard formula.

Truncated Cone Formula

A truncated cone (frustum) has the top cut off — leaving a large base radius (R) and smaller top radius (r):

V = (π × h ÷ 3) × (R² + R×r + r²)

Where:

• h = height of the truncated cone

• R = base radius (larger)

• r = top radius (smaller)

How the Cone Volume Calculator Works

Right / Oblique Cone

• Height (h) — enter in cm

• Radius (r) — enter in cm

• Volume — auto-calculated in cm³

The visual diagram updates to show a labeled cone with h and r marked for clarity.

Truncated Cone

• Height (h) — enter in cm

• Base radius (R) — the larger bottom radius, in cm

• Top radius (r) — the smaller top radius, in cm

• Volume — auto-calculated in cm³

The truncated cone diagram shows both R and h labeled on the frustum shape.

How to Calculate the Volume of a Cone — Step by Step

Example 1 — Standard Right Cone

Height = 9 cm, Radius = 3 cm

1. V = ⅓ × π × r² × h

2. V = ⅓ × 3.14159 × (3)² × 9

3. V = ⅓ × 3.14159 × 9 × 9

4. V = ⅓ × 254.469

5. V = 84.82 cm³

Example 2 — Using Diameter Instead of Radius

Diameter = 8 cm, Height = 12 cm

1. V = (1/12) × π × d² × h

2. V = (1/12) × 3.14159 × 64 × 12

3. V = (1/12) × 2,412.74

4. V = 201.06 cm³

Example 3 — Using Slant Height

Slant height (l) = 10 cm, Radius = 6 cm

1. Find height: h = √(l² − r²) = √(100 − 36) = √64 = 8 cm

2. V = ⅓ × π × 36 × 8

3. V = ⅓ × 904.78

4. V = 301.59 cm³

Example 4 — Truncated Cone

Height = 5 cm, Base radius R = 6 cm, Top radius r = 3 cm

1. V = (π × 5 ÷ 3) × (36 + 18 + 9)

2. V = (15.708) × (63)

3. V = 329.87 cm³

Cone Volume Quick Reference Table

All values calculated using V = ⅓πr²h

Fun Fact That'll Make You Laugh 😄

A standard ice cream cone holds approximately 20–30 cm³ of ice cream — which means if you filled it to a perfect mathematical cone shape with no overflow, you'd have about 2–3 tablespoons of ice cream.

Nobody in the history of ice cream has ever accepted a mathematically precise cone portion.

Physics invented the scoop. Mathematics invented the disappointment. 😂

Frequently Asked Questions

What is the volume of a cone in Class 9?

In Class 9 mathematics, the volume of a cone is taught as V = ⅓πr²h — where r is the base radius and h is the perpendicular height. It's introduced alongside cylinder and sphere volume formulas as part of surface area and volume chapters.

Why is a cone 1/3 the volume of a cylinder?

A cone is exactly one-third the volume of a cylinder with the same base and height because it takes precisely three identical cones to fill one cylinder — this can be demonstrated by filling a cone-shaped container with water and pouring it into an equivalent cylinder exactly three times. Mathematically it comes from integral calculus integration of the circular cross-sections from base to apex.

What is the real volume of a cone?

The real volume of a cone is calculated using V = ⅓ × π × r² × h — giving the exact cubic space enclosed inside. For example, a cone with radius 5 cm and height 10 cm has a volume of ⅓ × 3.14159 × 25 × 10 = 261.80 cm³.

What is the difference between a right cone and a truncated cone?

A right cone has a complete pointed apex directly above the center of the base. A truncated cone (frustum) has its top cut off parallel to the base — leaving two circular faces of different radii. The truncated cone uses a different formula: V = (πh/3)(R² + Rr + r²).

How do you find cone volume using slant height?

First calculate the perpendicular height using h = √(l² − r²), where l is the slant height and r is the base radius. Then apply the standard formula V = ⅓πr²h with the calculated height value.