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📐 Volume Calculators

Free online tools to calculate volume for 20+ geometric shapes. Step-by-step solutions, unit conversions, and visual diagrams included.

20+
Volume Calculators
100%
Free to Use
∞
Calculations

Welcome to our complete volume calculator collection! Whether you need to calculate the volume of a simple sphere or a complex partially-filled tank, we have the right tool for you. Each calculator includes interactive diagrams, multiple calculation modes, and step-by-step solutions.

All calculators support multiple units (metric and imperial) and provide instant results. Perfect for students, engineers, contractors, and anyone working with 3D shapes.

Basic 3D Shapes

Cube Calculator

Calculate cube volume, surface area, diagonal from side length

Rectangular Box

Volume, surface area, diagonal for boxes and boards

Sphere Calculator

Volume, surface area, circumference from radius or diameter

Cylinder Calculator

Volume, lateral area, total surface area for cylinders

Cone Calculator

Volume, slant height, surface area from radius and height

Pyramid Calculator

Volume for square, rectangular, triangular bases + frustums

Advanced 3D Shapes

Ellipsoid Calculator

Oblate, prolate, and triaxial ellipsoid volume calculations

Torus Calculator

Donut shape volume from major and minor radius

Capsule Calculator

Cylinder with hemispherical ends (stadium of revolution)

Wedge Calculator

Volume for wedge/ramp shapes with rectangular base

Polygon Prism

3 to 20-sided regular polygon base prisms

Revolved Trapezoid

Solid of revolution using Pappus theorem

Tanks & Containers

Horizontal Cylinder Tank

Partial fill volume for horizontal cylindrical tanks

Hollow Cylinder

Pipes, tubes, annular rings - material and capacity

Elliptical Tank

Oval cross-section horizontal tanks

Partial Sphere

Spherical cap volume for partially filled spheres

Trapezoid Tank

V-shaped troughs and trapezoidal prism tanks

Barrel Calculator

Wine, whiskey, and oil barrel volume with presets

Agricultural & Industrial

Grain Bin Calculator

Silos with cone roof, flat/hopper bottom, bushel conversion

Gravity Wagon

Agricultural wagon with hopper bottom, bushel output

Quick Formula Reference

Shape Volume Formula
Cube V = s³
Rectangular Box V = l × w × h
Sphere V = (4/3)πr³
Cylinder V = πr²h
Cone V = (1/3)πr²h
Pyramid V = (1/3)Ah
Ellipsoid V = (4/3)πabc
Torus V = 2π²Rr²
Capsule V = πr²(4r/3 + L)

Frequently Asked Questions

What is volume and how is it measured?
Volume is 3D space occupied by an object. Measured in cubic units: cm³, m³, liters, gallons, ft³, etc. Found by multiplying length × width × height for rectangular shapes.
Which volume calculator should I use?
Match the shape to your object. Rectangular box for boxes, cylinder for cans/pipes, sphere for balls, cone for funnels, etc. Use tank calculators for partial fill situations.
How do I convert between volume units?
Common conversions: 1 L = 1000 cm³ = 0.001 m³. 1 gal = 3.785 L = 231 in³. 1 ft³ = 7.48 gal = 28.3 L. Our calculators handle conversions automatically.
Why does 1/3 appear in cone and pyramid formulas?
Calculus result. Integration shows cones and pyramids have exactly 1/3 the volume of their enclosing cylinder or prism.
How do I calculate partially filled tank volume?
Use specialized tank calculators. Horizontal cylinder, partial sphere, and trapezoid tank calculators handle fill levels with proper curved surface formulas.
What is the difference between volume and capacity?
Volume = space occupied, capacity = amount it can hold. For containers, they're usually equal. Capacity often expressed in liters/gallons.
How accurate are these calculators?
Mathematically exact. They use standard geometric formulas with full precision. Real objects may differ due to manufacturing tolerances.
Can I calculate irregular shapes?
Break into simpler shapes. Divide complex objects into basic shapes, calculate each, then add (or subtract for holes).
What units should I use for input?
Any consistent unit. All dimensions must use the same unit. Our calculators support cm, m, in, ft and convert output automatically.
How do I find radius from diameter?
r = d/2. Radius is half the diameter. Most calculators accept either radius or diameter as input.
What is surface area vs volume?
Surface area = 2D outside, volume = 3D inside. Surface area in square units (cm²), volume in cubic units (cm³).
How do I calculate liquid capacity?
Calculate volume in cm³, convert to liters. 1 L = 1000 cm³. Or calculate in ft³ and multiply by 7.48 for gallons.
What is a frustum?
A truncated cone or pyramid. The portion remaining after cutting off the top with a parallel plane. Use pyramid calculator frustum mode.
How do I measure irregular containers?
Water displacement method. Fill with water, pour into measuring cup. 1 mL = 1 cm³. Or use closest geometric approximation.
What is the Pappus theorem?
V = 2π × centroid × Area. Elegant way to find volume of solids of revolution. Used in torus and revolved trapezoid calculators.
How do I calculate bushels for grain?
1 bushel = 1.244 ft³. Use grain bin or gravity wagon calculator. They output bushels automatically from dimensions.
Why use calculator vs manual calculation?
Speed, accuracy, unit conversion. Calculators eliminate arithmetic errors and handle complex formulas. Step-by-step solutions show the math.