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Volume CalculatorCalculate volume and surface area of 8 3D shapes — cube, sphere, cylinder, cone, and more.

Volume Calculator illustration
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Volume Calculator

Calculate volume and surface area of 8 3D shapes — cube, sphere, cylinder, cone, and more.

How to Use
1

Select 3D Shape

Choose from 8 three-dimensional shapes.

2

Enter Dimensions

Input the required measurements for your chosen shape.

3

View Results

See the calculated volume, surface area, and formula.

What Is Volume Calculator?

The Volume Calculator computes the volume and surface area of eight common three-dimensional shapes: cube, rectangular box, sphere, cylinder, cone, rectangular pyramid, ellipsoid, and torus. Select a shape, choose your unit of measurement, and enter the required dimensions. The calculator shows the volume in cubic units, the surface area in square units, and the formula used. This tool is essential for engineering, construction, shipping, and any task requiring 3D measurements.

Why Use Our Volume Calculator?

  • Eight 3D shapes including advanced forms (ellipsoid, torus)
  • Shows both volume and surface area
  • Multiple unit options (mm to yards)
  • Displays the formula used for each shape

Common Use Cases

Shipping & Packaging

Calculate box volumes for shipping cost estimation.

Construction

Determine concrete, soil, or fill material volumes.

Manufacturing

Calculate material volumes for casting, molding, and machining.

Education

Solve 3D geometry problems and verify calculations.

Technical Guide

Volume formulas: Cube: V = a³, SA = 6a². Box: V = lwh, SA = 2(lw+wh+lh). Sphere: V = (4/3)πr³, SA = 4πr². Cylinder: V = πr²h, SA = 2πr(r+h). Cone: V = (1/3)πr²h, SA = πr(r+√(r²+h²)). Pyramid: V = (1/3)lwh. Ellipsoid: V = (4/3)πabc, SA ≈ Knud Thomsen approximation. Torus: V = 2π²Rr², SA = 4π²Rr, where R is the major radius and r is the minor (tube) radius. Surface area of the ellipsoid uses the approximate formula with exponent 1.6075 for accuracy.

Tips & Best Practices

  • 1
    Volume is in cubic units: if inputs are in cm, output is in cm³
  • 2
    A sphere has the minimum surface area for a given volume among all 3D shapes
  • 3
    For irregular objects, water displacement is often the easiest volume measurement method
  • 4
    Surface area determines material needed for wrapping, painting, or coating

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Frequently Asked Questions

QHow do I convert cubic centimeters to liters?
1 liter = 1000 cm³ = 1000 mL. So divide cm³ by 1000 to get liters.
QHow do I calculate the volume of an irregular shape?
For irregular shapes, use water displacement (submerge the object and measure water displaced) or break the shape into simpler forms and sum the volumes.
QWhat is the difference between volume and capacity?
Volume is the amount of 3D space an object occupies. Capacity is the amount of substance a container can hold. They are related but differ for containers with wall thickness.
QHow much concrete do I need?
Calculate the volume in cubic meters or cubic yards. Concrete is typically ordered in cubic yards (US) or cubic meters (metric). Add 10% for waste.
QWhat is a torus?
A torus is a donut-shaped surface generated by rotating a circle around an axis. It has a major radius R (center to tube center) and minor radius r (tube radius).

About Volume Calculator

Volume Calculator is a free online tool from FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration required. No ads. Just fast, reliable tools.