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Mechanical Engineering3D

Cone Volume Calculator

Calculate volume of a cone or hopper from diameter and height, for silos, hoppers, and conical tank bottoms.

Inputs
Enter your values below
Result
Cone Volume
—
Enter values and click Calculate
Formula
π × (diameter ÷ 2)² × height ÷ 3 × 1000
Result unit: L

V_cone = (1/3)πr²h. ×1000 converts m³ to liters.

Introduction

Calculate the volume of a right circular cone — used for silo bottoms, hopper design, conical tank sections, and material flow calculations. A cone holds exactly 1/3 of the equivalent cylinder.

How This Calculator Works

V_cone = (1/3)πr²h. ×1000 converts m³ to liters.

Step-by-step process:

  1. Enter your input values in the calculator above
  2. The engine converts all inputs to SI base units (meters, kg, Pa)
  3. The formula is evaluated: pi * (diameter/2)^2 * height / 3 * 1000
  4. Result is formatted with the appropriate unit and precision

Calculation Example

4m diameter × 3m high cone = 12,566 liters.

Inputs: diameter=4, height=3
Result: 12566 L

Unit Conversion for Cone Volume

**Volume units**

- 1 m³ = 1000 L = 35.315 ft³

- 1 ft³ = 0.02832 m³ = 28.317 L

- 1 US gal = 3.785 L

**Length units**

- 1 m = 3.28084 ft

- 1 inch = 25.4 mm

Cone volume V = (1/3)πr²h requires consistent length units. For a frustum (truncated cone), V = (πh/3)(R² + Rr + r²). Convert radius and height to the same unit before computing.

Engineering Applications

  • •Silo design
  • •Hopper volume
  • •Cone bottom tanks
  • •Material handling

Frequently Asked Questions

What about a truncated cone (frustum)?

Frustum volume = (πh/3)(R² + Rr + r²) where R and r are the two radii. This calculator handles full cones only.

How much angle for mass flow in a hopper?

For most bulk solids, a hopper half-angle of 15-20° from vertical ensures mass flow. Steeper for sticky materials.

How do I convert cone volume between m³ and ft³?

1 m³ = 35.315 ft³. For example, a 2 m³ hopper = 70.6 ft³. Conversely, divide ft³ by 35.315 to get m³.

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Cylinder Volume CalculatorSphere Volume CalculatorPressure Vessel Volume CalculatorTank Volume CalculatorTank Capacity CalculatorTank Surface Area CalculatorTank Weight CalculatorStorage Capacity CalculatorPartially Filled Horizontal Tank Volume Calculator

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Engineering Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.
Reviewed by: Industrial Engineering Team
References: ASME B31.3, ASTM A36, Perry's Chemical Engineers' Handbook