Math calculators

Volume Calculator

Updated May 20, 2026 By Jehan Wadia
Sphere
r
V = (4/3)πr³
Diameter = 2 × Radius
Results
Volume: 523.5988 m³
Cone
h r
V = (1/3)πr²h
Results
Volume: 65.9734 m³
Cube
a
V = a³
Results
Volume: 64.0000 m³
Cuboid / Rectangular Prism
h l w
V = l × w × h
Results
Volume: 30.0000 m³
Cylinder
r h
V = πr²h
Results
Volume: 282.7433 m³
Capsule
r h
V = πr²h + (4/3)πr³
Height of the cylindrical portion only.
Results
Volume: 108.9101 m³
Spherical Cap
r h R = ball radius
V = (πh²/3)(3R − h) = (πh/6)(3r² + h²)
Enter any 2 of the 3 values. The third will be computed automatically.
Results
Volume:
Conical Frustum
r₁ r₂ h
V = (πh/3)(r₁² + r₂² + r₁r₂)
Results
Volume: 326.7256 m³
Ellipsoid
a b c
V = (4/3)πabc
Results
Volume: 125.6637 m³
Square Pyramid
h a
V = (1/3)a²h
Results
Volume: 108.0000 m³
Tube / Hollow Cylinder (Pipe)
D_o D_i
V = π × L × (D_o² − D_i²) / 4
Results (Material Volume)
Volume: 565.4867 m³
Pyramid (General)
h Base Area
V = (1/3) × Base Area × h
Enter the area of the base in square units.
Results
Volume: 100.0000 m³
Volume Comparison Across All Shapes

Introduction

Volume is the amount of space inside a 3D shape. Whether you need to find how much water fits in a tank, how much concrete fills a mold, or how much air is inside a ball, knowing the volume gives you the answer. Each shape has its own formula. A sphere uses V = (4/3)πr³, a cube uses V = a³, and a cylinder uses V = πr²h. Remembering every formula and doing the math by hand takes time and leaves room for mistakes.

This volume calculator does the work for you. It covers 12 common shapes: sphere, cone, cube, cuboid, cylinder, capsule, spherical cap, conical frustum, ellipsoid, square pyramid, tube, and general pyramid. Just pick a shape, type in your measurements, and choose your units. The tool gives you the volume in cubic meters right away, then converts it into cubic centimeters, liters, gallons, cubic feet, and more. You can switch between radius and diameter, mix different units across inputs, and compare all your results side by side on a bar chart. Hit "Calculate All" to update every shape at once, or let the calculator update live as you type.

How to Use Our Volume Calculator

Enter the measurements for any 3D shape below, and the calculator will give you the volume in cubic meters along with conversions to other units. You can calculate volume for all 12 shapes at once.

Sphere: Enter the radius or diameter of the sphere. Use the toggle to switch between radius and diameter input. Pick your unit of measurement from the dropdown. For a dedicated tool focused only on spheres, try our Sphere Volume Calculator.

Cone: Enter the radius (or diameter) of the base and the height of the cone. Toggle between radius and diameter as needed, and choose your preferred unit for each value. You can also use our standalone Cone Volume Calculator for more detail.

Cube: Enter the side length of the cube. Since all sides of a cube are equal, only one measurement is needed. Select your unit from the dropdown.

Cuboid (Rectangular Prism): Enter the length, width, and height of the box shape. Each dimension can use a different unit if needed. If you need to figure out the volume in cubic feet specifically, our Cubic Feet Calculator can help.

Cylinder: Enter the radius (or diameter) of the circular base and the height of the cylinder. Use the toggle to switch between radius and diameter. We also have a dedicated Cylinder Volume Calculator for cylinder-specific calculations.

Capsule: Enter the radius (or diameter) and the height of the cylindrical middle section only. The two rounded half-sphere ends are calculated automatically from the radius.

Spherical Cap: Enter any 2 of the 3 values — base radius (r), ball radius (R), or height (h). The calculator will figure out the missing third value and compute the volume for you.

Conical Frustum: Enter the top radius (r₁), bottom radius (r₂), and the height. You can toggle between radius and diameter input for both the top and bottom circles.

Ellipsoid: Enter the three semi-axis lengths — A, B, and C. These are the distances from the center to the surface along each of the three directions.

Square Pyramid: Enter the base edge length (one side of the square base) and the height from the base to the tip of the pyramid.

Tube (Hollow Cylinder): Enter the outer diameter, inner diameter, and the length of the tube. The inner diameter must be smaller than the outer diameter. The result shows the volume of the material only, not the hollow space inside. For pipe-specific applications, check out the Pipe Volume Calculator.

Pyramid (General): Enter the base area in square units and the height. This works for any pyramid shape — triangular, pentagonal, or irregular — as long as you know the area of the base. If you need help finding that base area, our Area Calculator can compute it for you.

What Is Volume?

Volume is the amount of three-dimensional space that an object takes up. Think of it as how much water you would need to completely fill a shape. Volume is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or liters (L). It is one of the most important measurements in math, science, and everyday life.

How Volume Is Calculated

Every 3D shape has its own formula for finding volume. These formulas use measurements like radius, height, length, and width. Here are the shapes covered by this calculator and how their volumes work:

  • Sphere: A perfectly round ball. Its volume is V = (4/3)πr³, where r is the radius. The radius is the distance from the center to the edge.
  • Cone: A shape with a circular base that narrows to a point. Its volume is V = (1/3)πr²h. A cone holds exactly one-third the volume of a cylinder with the same base and height.
  • Cube: A box where all sides are equal. Its volume is simply V = a³, where a is the side length. You can use our Exponent Calculator to quickly compute cubed values.
  • Cuboid (Rectangular Prism): A box shape with different length, width, and height. Its volume is V = l × w × h.
  • Cylinder: A shape like a can or pipe. Its volume is V = πr²h. You find the area of the circular base and multiply it by the height.
  • Capsule: A cylinder with half-sphere caps on each end. Its volume combines a cylinder and a full sphere: V = πr²h + (4/3)πr³.
  • Spherical Cap: A dome-shaped slice cut from a sphere. You only need two of the three values (base radius, ball radius, or height) to find its volume.
  • Conical Frustum: A cone with the top cut off. Its formula is V = (πh/3)(r₁² + r₂² + r₁r₂), using both the top and bottom radii.
  • Ellipsoid: A stretched or squished sphere, like an egg. Its volume is V = (4/3)πabc, where a, b, and c are the three semi-axes.
  • Square Pyramid: A pyramid with a square base. Its volume is V = (1/3)a²h.
  • Tube (Hollow Cylinder): A pipe shape with empty space inside. The volume of material equals the outer cylinder minus the inner cylinder.
  • General Pyramid: Any pyramid shape where you already know the base area. Its volume is V = (1/3) × Base Area × h.

Why Volume Matters

Knowing how to find volume is useful in many real situations. You need volume when filling a swimming pool, shipping a package, pouring concrete, measuring medicine doses, or figuring out how much soil fits in a garden bed. Engineers, builders, scientists, and cooks all use volume calculations regularly. Construction professionals often need to convert volumes into cubic yards for ordering materials like gravel, sand, or mulch.

Tips for Accurate Results

Always make sure your measurements use the same unit before calculating. For example, if your radius is in centimeters and your height is in meters, the answer will be wrong. This calculator handles unit conversion automatically, so you can enter each measurement in whatever unit is easiest for you. It will convert everything to meters behind the scenes and then show results in ten different volume units, including liters, gallons, cubic feet, and more.

Remember that the radius is half the diameter. If you only know the diameter of a circle, you can switch the input mode from "Radius" to "Diameter" and enter it directly without doing the division yourself.

If you're working with 2D shapes instead, you may find our Circle Area Calculator, Triangle Area Calculator, or Area of a Rectangle Calculator helpful. For related 3D calculations, our Surface Area Calculator computes the outer surface of common shapes, and our Density Calculator lets you find mass from volume when you know the material's density. You might also find our Square Footage Calculator useful for flat area measurements before extending them into volume.


Frequently asked questions

What units can I use in the volume calculator?

You can use kilometers, meters, centimeters, millimeters, micrometers, nanometers, angstroms, miles, yards, feet, and inches. The calculator converts everything to meters behind the scenes. Your results show up in 10 volume units including cubic meters, cubic centimeters, liters, milliliters, US gallons, US quarts, cubic feet, cubic inches, and cubic yards.

Can I use different units for different measurements in the same shape?

Yes. Each input field has its own unit dropdown. For example, you can enter a cylinder's radius in centimeters and its height in feet. The calculator converts each value to meters before doing the math, so the answer is always correct.

What is the difference between radius and diameter?

The radius is the distance from the center of a circle to its edge. The diameter is the distance all the way across the circle through the center. The diameter is always twice the radius. If you know the diameter, toggle the input to "Diameter" so you don't have to divide by 2 yourself.

Does the calculator update automatically or do I need to press a button?

The calculator updates live as you type. You do not need to press any button. However, you can also press the "Calculate All" button to recalculate every shape at once if you want.

What does the Reset button do?

The Reset button sets all input fields back to their original default values. It also switches all units back to meters and sets all toggles back to radius mode. Then it recalculates everything fresh.

How does the spherical cap section work with only 2 values?

A spherical cap has three related values: base radius (r), ball radius (R), and height (h). If you know any two, the calculator figures out the third one using geometry. Just fill in two fields and leave the third blank. The missing value and the volume will both appear in the results.

What does the tube calculator measure?

The tube calculator measures the volume of the material in a hollow cylinder or pipe. It does not measure the empty space inside the tube. It subtracts the inner cylinder from the outer cylinder to give you just the wall material volume.

Why does the tube calculator say inner diameter must be less than outer diameter?

The inner hole of a tube must be smaller than the outside of the tube. If the inner diameter is equal to or larger than the outer diameter, the tube cannot physically exist. The calculator shows an error to let you know your numbers need to be fixed.

What is the general pyramid calculator for?

The general pyramid calculator works for any pyramid shape, not just square-based ones. You enter the area of the base and the height. This lets you calculate volume for triangular pyramids, pentagonal pyramids, or any irregular pyramid as long as you know the base area.

What does the bar chart at the bottom show?

The bar chart compares the volumes of all 12 shapes side by side in cubic meters. It updates every time you change a value. This makes it easy to see which shape has the most or least volume based on your current inputs.

How do I calculate the volume of a capsule?

Enter the radius (or diameter) and the height of the straight cylindrical middle section only. Do not include the rounded ends in the height. The calculator adds the volume of the cylinder part and the volume of a full sphere (from the two half-sphere caps) automatically.

What is the difference between a cuboid and a cube?

A cube has all sides the same length. A cuboid (also called a rectangular prism) can have different lengths, widths, and heights. A cube is a special type of cuboid where all three measurements are equal.

What are semi-axes on an ellipsoid?

Semi-axes are the three distances from the center of the ellipsoid to its surface along each direction. Think of it like three different radii. If all three are equal, the ellipsoid is a perfect sphere. If they differ, the shape is stretched or squished.

Can I enter decimal numbers?

Yes. All input fields accept decimal numbers. For example, you can enter 3.5 meters for a radius or 12.75 centimeters for a height. The calculator handles decimals with full precision.

What happens if I enter zero or a negative number?

The calculator will show a dash (—) instead of a result. Volume requires positive measurements. A side length, radius, or height of zero or less does not make a real 3D shape, so no volume can be calculated.

How is a conical frustum different from a cone?

A cone comes to a point at the top. A conical frustum is a cone with the top sliced off, leaving a smaller flat circle on top and a larger flat circle on the bottom. You need both the top radius and bottom radius plus the height to find its volume.