Volume Calculator — Free Online Volume Calculator

How to Use the Volume Calculator

1. Select a 3D shape: Choose from the dropdown menu: Sphere, Cube, Cylinder, Cone, or Rectangular Prism. The input fields automatically adjust to show the required dimensions for the selected shape.
2. Enter the dimensions: Type the required measurements into the input fields. Spheres need only the radius. Cubes need only the side length. Cylinders and cones need radius and height. Rectangular prisms need length, width, and height. All values must be positive.
3. Read the volume: The results panel instantly shows the calculated volume in cubic units along with the formula used. Results update in real time as you change any input value, so you can experiment with different dimensions freely.

The calculator works with any unit system. If you enter measurements in centimeters, the volume will be in cubic centimeters. If you enter in feet, the result is in cubic feet. Ensure all inputs use the same unit for accurate results.

Volume Formulas for All Shapes

Variables Explained

• r (Radius): For spheres, cylinders, and cones, the distance from the center of the base circle to its edge.
• s (Side Length): For cubes, the length of any edge. All 12 edges of a cube are equal.
• h (Height): For cylinders, cones, and rectangular prisms, the vertical distance between the top and bottom faces.
• l (Length), w (Width): For rectangular prisms, the two dimensions of the base rectangle.
• π (Pi): The mathematical constant approximately 3.14159, used in all formulas involving circular cross-sections.

Step-by-Step Example (Cylinder)

Calculate the volume of a cylinder with radius 3 and height 8:

1. Identify the values: r = 3, h = 8
2. Calculate the base area: π x r² = π x 9 = 28.27
3. Multiply by the height: 28.27 x 8 = 226.19 cubic units

The cylinder volume formula can be thought of as "base area times height." This principle extends to any prism-like shape: the volume equals the cross-sectional area multiplied by the height (or depth).

Practical Examples

Example 1: Tyler's Swimming Pool

Tyler is filling his rectangular swimming pool that measures 30 feet long, 15 feet wide, and 5 feet deep. He needs to know how many gallons of water it holds and the estimated fill time.

• Shape: Rectangular Prism, l = 30 ft, w = 15 ft, h = 5 ft
• Volume = 30 x 15 x 5 = 2,250 cubic feet
• In gallons: 2,250 x 7.481 = 16,832 gallons

Tyler's pool holds approximately 16,832 gallons of water. At a typical garden hose flow rate of 9 gallons per minute, filling would take about 1,870 minutes (approximately 31 hours). A fire hydrant at 250 gallons per minute could fill it in about 67 minutes. Water cost varies by region, but at $0.005 per gallon, the water costs approximately $84.

Example 2: Hannah's Ice Cream Cone

Hannah is designing packaging for waffle cones. Each cone has a radius of 1.5 inches at the top and a height of 5.5 inches. She needs to know how much ice cream each cone can hold.

• Shape: Cone, r = 1.5 in, h = 5.5 in
• Volume = (1/3) x π x 1.5² x 5.5 = (1/3) x π x 2.25 x 5.5 = 12.96 cubic inches
• In fluid ounces: 12.96 / 1.805 ≈ 7.18 fl oz

Each cone holds approximately 12.96 cubic inches or about 7.18 fluid ounces of ice cream. Since ice cream is typically served with a scoop on top that extends above the cone rim, the actual serving would be larger. A standard scoop is a hemisphere with radius about 1.25 inches, adding about 4.09 cubic inches (approximately 2.27 fl oz) for a total of roughly 9.45 fl oz per serving.

Example 3: Derek's Water Tank

Derek is installing a cylindrical rainwater collection tank. The tank has a diameter of 4 feet and a height of 6 feet. He wants to know its capacity in gallons.

• Shape: Cylinder, r = 4/2 = 2 ft, h = 6 ft
• Volume = π x 2² x 6 = π x 4 x 6 = 75.40 cubic feet
• In gallons: 75.40 x 7.481 = 564.05 gallons

Derek's tank holds approximately 564 gallons of rainwater. For reference, the average US household uses about 300 gallons per day. This tank could supply nearly two days of household water, or significantly more if used only for irrigation. Rainwater collection tanks are an excellent addition to sustainable home design. For calculating the surface area of the tank (for painting or insulation), try our surface area calculator.

Example 4: Olivia's Spherical Aquarium

Olivia is purchasing a spherical fish tank with a diameter of 16 inches. She needs to know the volume to determine appropriate filtration and fish capacity.

• Shape: Sphere, r = 16/2 = 8 in
• Volume = (4/3) x π x 8³ = (4/3) x π x 512 = 2,144.66 cubic inches
• In gallons: 2,144.66 / 231 = 9.28 gallons

The spherical tank holds approximately 9.28 gallons. Following the general rule of 1 inch of fish per gallon, Olivia could comfortably house about 7-8 small fish (accounting for partial filling and decorations reducing usable volume). The spherical shape provides a unique viewing experience but requires specialized filtration compared to standard rectangular aquariums.

Volume Formula Quick Reference Table

Tips and Complete Guide

Volume-to-Capacity Conversions

Converting volume to liquid capacity is essential for many practical applications. Key conversions: 1 cubic foot = 7.481 US gallons. 1 cubic meter = 264.172 US gallons = 1,000 liters. 1 US gallon = 231 cubic inches. 1 liter = 61.024 cubic inches. For water weight: 1 cubic foot of water = 62.4 pounds, 1 cubic meter = 1,000 kg, 1 US gallon = 8.34 pounds. These conversions are critical for aquariums, pools, tanks, and plumbing calculations.

The Cavalieri Principle

The Cavalieri Principle states that if two solids have the same height and the same cross-sectional area at every level, they have the same volume. This means a tilted cylinder (oblique cylinder) has the same volume as a straight (right) cylinder with the same base radius and height. Similarly, a pyramid with any base shape has volume = (1/3) x base area x height. This principle simplifies volume calculations for shapes that might appear complex at first glance.

Scaling and Volume

Volume scales with the cube of the linear dimension. If you double all dimensions of a shape, its volume increases by a factor of 8 (2 cubed). If you triple all dimensions, volume increases by a factor of 27 (3 cubed). This cubic scaling explains why large animals need proportionally thicker bones (volume and weight grow faster than cross-sectional area) and why small containers are proportionally less efficient than large ones for storage.

Practical Measurement Tips

For cylindrical objects like cans, pipes, and tanks, measure the diameter across the top and divide by 2 for the radius. For height, measure the inside dimension if you need the internal volume. For irregular containers, fill with water and pour into a measuring cup to find the volume directly. For rooms and boxes, measure inside dimensions for capacity calculations and outside dimensions for shipping or space planning.

Common Mistakes to Avoid

• Confusing radius with diameter: Most real-world measurements use diameter (pipe sizes, tank sizes). Always divide by 2 to get the radius before using volume formulas. Using diameter instead of radius makes your answer 8 times too large for spheres and 4 times too large for cylinders.
• Forgetting the 1/3 factor for cones: A cone has one-third the volume of a cylinder with the same base and height. Forgetting this factor makes your answer three times too large. The same 1/3 factor applies to all pyramids.
• Mixing cubic and square units: Volume uses cubic units (cubic feet, cubic meters). Area uses square units. If your answer seems too large or small, check whether you are computing volume (3D) or area (2D).
• Not cubing the radius for spheres: The sphere formula uses r cubed, not r squared. A sphere with radius 10 has volume = (4/3) x pi x 1000 = 4188.79, not (4/3) x pi x 100 = 418.88.
• Using slant height for cones instead of vertical height: The cone volume formula uses the vertical (perpendicular) height from base to apex, not the slant height along the side. If you know the slant height l and radius r, calculate height: h = sqrt(l squared - r squared).

Frequently Asked Questions