IES
Mechanical EngineeringP0

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.

Calculation Example

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

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

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.

Related Calculators

Cylinder Volume CalculatorSphere Volume Calculator

Need engineering design support?

Our engineering team validates results like these with full multi-disciplinary design review. Beyond the Cone Volume Calculator, we deliver build-ready engineering.

  • Industrial Building Design
  • Structural Optimization
  • HVAC & MEP Engineering
  • Chemical & Energy Projects
Request Engineering Assessment
Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.