Cone Volume Calculator
Calculate the volume of a cone quickly and accurately using the radius, diameter, height, or slant height. Perfect for students, teachers, engineers, and DIY projects. Get results in multiple units with a visual breakdown.
What Is a 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 base is a circle, and the distance from the center of the base to the apex is the height. The distance from the apex to any point on the edge of the base along the surface is the slant height.
The volume of a cone is the amount of space enclosed by its surface. It is exactly one-third of the volume of a cylinder with the same base and height: V = ⅓ × π × r² × h.
How Does the Cone Volume Calculator Work?
The calculator uses standard cone formulas:
From Radius and Height: V = ⅓ × π × r² × h
From Diameter and Height: V = ⅓ × π × (d/2)² × h = π × d² × h / 12
From Slant Height: First find height: h = √(s² − r²), then V = ⅓ × π × r² × h
Where:
r = Radius of the base
d = Diameter of the base
h = Height (perpendicular from base to apex)
s = Slant height
π ≈ 3.14159
Simply choose your input method (radius & height, diameter & height, or slant height), enter the values, and the calculator will instantly compute the volume. It will also show you the radius, diameter, height, and slant height for reference.
Why Use This Cone Volume Calculator?
- Three Input Methods: Enter radius & height, diameter & height, or slant height.
- Unit Flexibility: Switch between metric (m, cm) and imperial (ft, in).
- All Measurements: See radius, diameter, height, slant height, and volume simultaneously.
- Multiple Output Units: View volume in cubic meters, cubic feet, cubic inches, liters, and gallons.
- Free & Private: No registration, no data storage.
Real-World Applications of Cone Volume
- Construction: Calculating the volume of concrete for cone-shaped structures.
- Manufacturing: Determining the capacity of conical hoppers and funnels.
- Food & Beverage: Measuring the volume of ice cream cones and packaging.
- Engineering: Calculating the volume of conical tanks and silos.
- Education: Learning geometry and solving math problems.
❓ Cone Volume Calculator FAQ
What is the formula for the volume of a cone?
The formula is V = ⅓ × π × r² × h, where V is the volume, π (pi) is approximately 3.14159, r is the radius of the base, and h is the height of the cone.
How do I calculate the volume of a cone from the radius and height?
Use the formula V = ⅓ × π × r² × h. For example, if the radius is 5 cm and the height is 10 cm, the volume is ⅓ × 3.14159 × 25 × 10 = 261.80 cm³. This calculator does this for you automatically.
How do I calculate the volume of a cone from the diameter and height?
Divide the diameter by 2 to get the radius, then use V = ⅓ × π × r² × h. Alternatively, use V = π × d² × h / 12. For example, a diameter of 10 cm gives a radius of 5 cm, so the volume is 261.80 cm³.
How do I calculate the volume of a cone from the slant height?
First find the height using the Pythagorean theorem: h = √(s² − r²), where s is the slant height and r is the radius. Then use V = ⅓ × π × r² × h. For example, if the radius is 5 cm and the slant height is 11.18 cm, the height is √(125 − 25) = 10 cm, so the volume is 261.80 cm³.
What is the difference between height and slant height?
The height is the perpendicular distance from the base to the apex. The slant height is the distance from the apex to any point on the edge of the base along the surface. The slant height is always longer than the height.
What is the relationship between the volume of a cone and a cylinder?
A cone with the same base and height as a cylinder has exactly one-third of the cylinder's volume. This is because V_cylinder = π × r² × h and V_cone = ⅓ × π × r² × h.
What is the volume of a cone with radius 3 and height 4?
Volume = ⅓ × π × 3² × 4 = ⅓ × 3.14159 × 9 × 4 = 37.70 cubic units.
What is the volume of a cone with diameter 8 and height 6?
Radius = 8/2 = 4. Volume = ⅓ × π × 4² × 6 = ⅓ × 3.14159 × 16 × 6 = 100.53 cubic units.
What is the volume of a cone with radius 4 and slant height 5?
Height = √(5² − 4²) = √(25 − 16) = √9 = 3. Volume = ⅓ × π × 4² × 3 = ⅓ × 3.14159 × 16 × 3 = 50.27 cubic units.
How do I convert cubic meters to liters?
1 cubic meter = 1000 liters. The calculator automatically converts between units and displays volume in liters and gallons.
How do I convert cubic feet to gallons?
1 cubic foot ≈ 7.48052 gallons. The calculator shows volume in gallons for imperial units.
What is the difference between a right cone and an oblique cone?
A right cone has its apex directly above the center of the base. An oblique cone has its apex offset from the center. This calculator calculates the volume of a right cone.
What is the volume of a cone in terms of diameter?
The volume in terms of diameter is V = π × d² × h / 12. For example, a cone with diameter 8 and height 6 has volume π × 64 × 6 / 12 = 100.53 cubic units.
How do I find the radius of a cone if I know the volume and height?
Rearrange the formula: r = √(3V / (π × h)). For example, if the volume is 100 and the height is 6, r = √(300 / (π × 6)) = √(15.915) = 3.99 units.
How do I find the height of a cone if I know the volume and radius?
Rearrange the formula: h = 3V / (π × r²). For example, if the volume is 100 and the radius is 4, h = 300 / (π × 16) = 300 / 50.27 = 5.97 units.
What units can I use for cone measurements?
You can use meters (m), centimeters (cm), feet (ft), inches (in), or any other unit of length. The volume will be in cubic units (m³, cm³, ft³, in³). This calculator supports metric and imperial systems.
How do I calculate the volume of a cone with a rounded base?
A cone typically has a flat circular base. If the base is rounded, it's not a standard cone. This calculator calculates the volume of a standard right circular cone.
How do I calculate the volume of a frustum of a cone?
A frustum is a cone with the top cut off. The formula is V = ⅓ × π × h × (R² + Rr + r²), where R is the larger radius, r is the smaller radius, and h is the height. This calculator focuses on the volume of a full cone.
Is this calculator free to use?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.