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Mechanical Engineering3D

Sphere Volume Calculator

Calculate volume and surface area of a sphere for spherical tanks, LPG/propane storage vessels, and pressure vessels.

Inputs
Enter your values below
Result
Sphere Volume
—
Enter values and click Calculate
Formula
4 ÷ 3 × π × (diameter ÷ 2)³ × 1000
Result unit: L

V = (4/3)πr³ = πD³/6. ×1000 converts m³ to liters. Spheres are optimal for pressurized storage (minimum wall stress per unit volume).

Introduction

Calculate volume of a sphere from diameter. Spherical tanks are widely used for LPG, propane, butane, and cryogenic storage because their shape provides uniform stress distribution under pressure, minimizing wall thickness requirements.

How This Calculator Works

V = (4/3)πr³ = πD³/6. ×1000 converts m³ to liters. Spheres are optimal for pressurized storage (minimum wall stress per unit volume).

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: 4/3 * pi * (diameter/2)^3 * 1000
  4. Result is formatted with the appropriate unit and precision

Calculation Example

10m diameter sphere = 523,599 liters (~524 m³) — typical small LPG sphere.

Inputs: diameter=10
Result: 523599 L

Unit Conversion for Sphere Volume

**Volume units**

- 1 m³ = 1000 L = 264.17 US gal = 35.315 ft³

- 1 US gal = 3.785 L

- 1 bbl (oil) = 0.159 m³

**Length units**

- 1 m = 3.28084 ft

- 1 inch = 25.4 mm

Sphere volume V = (4/3)πr³ requires consistent length units. Convert the radius to the same unit as the desired volume before computing, then convert the result to m³, L, or gallons as needed.

Engineering Applications

  • •LPG/propane storage
  • •Cryogenic tanks
  • •Gas holders
  • •Pressure vessels

Frequently Asked Questions

Why use spherical tanks for pressurized storage?

A sphere has minimum surface area per unit volume and uniform membrane stress distribution, requiring less steel than a cylinder for the same pressure and volume.

What are standard sphere sizes?

Common sizes range from 100 m³ (6m diameter) to 10,000 m³+ (27m diameter) for refinery and petrochemical applications.

How do I convert sphere volume between m³ and gallons?

1 m³ = 264.17 US gallons. For example, a 1000 m³ sphere = 264,170 US gallons. Convert using this factor for storage planning.

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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