Free Volume of Cone Calculator – Accurate, Instant & Ad-Free

Volume of Cone Calculator

Find the volume of any cone instantly with our Free Volume of Cone Calculator. Whether you’re working on geometry homework, designing containers, or performing engineering calculations, this tool provides fast and precise results — all in one click.

At Digital Calculator, we make geometry simple, visual, and reliable. Our Volume of Cone Calculator accurately computes the volume of right circular cones, oblique cones, and even truncated (frustum) cones using any given set of inputs: radius, height, or slant height.

No manual calculations, no errors — just instant accuracy

What Is the Volume of a Cone?

A cone is a three-dimensional solid with a circular base and a single vertex that tapers to a point. You can think of it like an ice cream cone, traffic cone, or funnel — each representing a perfect geometric cone in real life.

The volume of a cone measures how much space it occupies or how much material it can hold. It’s expressed in cubic units, such as cm³, m³, in³, or ft³.

Because a cone is essentially one-third of a cylinder with the same base and height, its volume formula is derived directly from the cylinder volume formula.

Volume of a Cone Formula

The standard formula for the volume of a right circular cone is:

Volume = (1/3) × π × r² × h

Where:

• r = radius of the circular base
• h = height of the cone
• π (pi) ≈ 3.1416

This formula applies to any cone where the vertex is directly above the center of the base (a right cone).

Example:

If a cone has a radius of 6 cm and height of 12 cm:
Volume = (1/3) × π × 6² × 12
= (1/3) × 3.1416 × 36 × 12
= (1/3) × 1357.17
= 452.39 cm³

 Result: The volume of the cone is 452.39 cubic centimeters.

Alternative Volume Formulas for Different Cone Types

The formula can be adapted depending on which values you know — radius, slant height, diameter, or even if it’s a truncated cone.

Our Volume of Cone Calculator supports all these automatically.

1. Using Radius and Height

Formula:
V = (1/3) × π × r² × h

This is the simplest and most common method.

Example:
r = 5 cm, h = 9 cm
V = (1/3) × 3.1416 × 25 × 9 = 235.62 cm³

 Result: 235.62 cm³

2. Using Diameter and Height

Since diameter = 2r, the formula becomes:
 V = (1/12) × π × d² × h

Example:
d = 10 cm, h = 15 cm
V = (1/12) × 3.1416 × 100 × 15 = 392.7 cm³

 Result: 392.7 cm³

3. Using Slant Height and Height

If you know the slant height (l) and vertical height (h), you can first find the radius using the Pythagorean theorem:
 r = √(l² – h²)
Then apply:
 V = (1/3) × π × r² × h

Example:
l = 13 cm, h = 12 cm
r = √(13² – 12²) = √(169 – 144) = √25 = 5 cm
V = (1/3) × 3.1416 × 5² × 12 = 314.16 cm³

 Result: 314.16 cm³

4. Volume of a Frustum (Truncated Cone)

When a cone is cut parallel to its base, it forms a frustum. The formula is:

V = (1/3) × π × h × (r₁² + r₂² + r₁r₂)

Where:

• r₁ = radius of the larger base
• r₂ = radius of the smaller base
• h = height of the frustum

Example:
r₁ = 8 cm, r₂ = 4 cm, h = 10 cm
V = (1/3) × 3.1416 × 10 × (64 + 16 + 32)
= (1/3) × 3.1416 × 10 × 112
= 1172.86 cm³

 Result: 1172.86 cm³

How to Use the Free Volume of Cone Calculator

Using our calculator is quick, simple, and intuitive:

1. Select your input type — radius & height, diameter, slant height, or frustum.
2. Enter the known values.
3. Click “Calculate.”
4. Get the instant result in cubic units with step-by-step breakdowns.

You can also switch between metric and imperial units for convenience.

 Try the Free Volume of Cone Calculator on Digital Calculator — precise, fast, and completely ad-free.

Step-by-Step Examples

Let’s look at a few real-world examples to see how this formula works across scenarios.

Example 1: Ice Cream Cone

Radius = 3.5 cm, Height = 9 cm
V = (1/3) × π × 3.5² × 9
= (1/3) × 3.1416 × 12.25 × 9
= 115.45 cm³

 Result: 115.45 cubic centimeters of ice cream.

Example 2: Water Tank Cone Section

Diameter = 16 m, Height = 10 m
V = (1/12) × 3.1416 × 16² × 10
= (1/12) × 3.1416 × 256 × 10
= 670.2 m³

 Result: 670.2 cubic meters.

Example 3: Hollow Frustum

r₁ = 5 m, r₂ = 3 m, h = 12 m
V = (1/3) × π × 12 × (25 + 9 + 15) = (1/3) × 3.1416 × 12 × 49 = 615.75 m³

 Result: 615.75 cubic meters.

Volume of Cone Formula Summary Table

Our calculator automatically identifies the formula based on your inputs and ensures accurate results every time.

Understanding Cone Geometry

To fully understand how cone volume works, let’s break down its key parts:

• Base: A circle at the bottom of the cone.
• Height (h): The perpendicular distance from the base to the apex.
• Slant height (l): The length of the side, measured from the apex to any point on the base edge.
• Radius (r): Distance from the center of the base to its edge.

The cone’s volume formula — (1/3)πr²h — tells us that the cone has one-third the volume of a cylinder with the same base and height.

Real-Life Applications of Cone Volume

The cone volume formula has numerous practical uses across industries and education.

1. Construction & Architecture

Used to determine the volume of conical structures like silos, domes, funnels, or roof elements.

2. Engineering & Manufacturing

Helps design machine parts, tanks, and components with cone-like geometry.

3. Education

Essential for geometry and calculus lessons involving solid figures and spatial reasoning.

4. Food & Packaging

Used in designing conical containers like ice cream cones, cups, and dispensers.

5. Science & Astronomy

Applied in estimating the volume of conical projections, volcanoes, or other natural formations.

No matter your use case, our Free Volume of Cone Calculator makes every calculation effortless.

Common Mistakes to Avoid

Even simple geometry can go wrong with small errors. Avoid these common mistakes:

1. Mixing up diameter and radius — radius = diameter ÷ 2.
2. Using slant height instead of height — unless specified, height must be perpendicular to the base.
3. Inconsistent units — always convert all measurements to the same unit (e.g., cm, m, ft).
4. Forgetting the 1/3 factor — the cone’s volume is one-third of a cylinder’s.
5. Rounding too early — round off only after the final calculation.

Our calculator handles these issues automatically — ensuring every result is perfectly accurate.

Why Use Digital Calculator’s Volume of Cone Tool

Our Volume of Cone Calculator is built for accuracy, simplicity, and educational value.

Here’s why users trust Digital Calculator:

•  Completely Free & Ad-Free — no logins, no interruptions
•  Multiple Calculation Methods — radius, diameter, slant, or frustum
•  Instant Results — powered by precision π constants
•  Unit Conversion Support — cm³, m³, ft³, and in³
•  Step-by-Step Breakdown — learn while you calculate
•  Mobile-Friendly Interface — use it anywhere, anytime

 Try the Free Volume of Cone Calculator today — accuracy made simple with Digital Calculator.

Why Choose Digital Calculator

At Digital Calculator, we believe math should be simple, visual, and accurate. Every tool we offer is:

• 100% free and ad-free
• Designed for students, engineers, and everyday users
• Optimized for learning, not just computing

 Calculate now with Digital Calculator — precision made easy and always free!