Volume Calculator

Calculate the volume of common 3D shapes instantly with full step-by-step solutions. Choose from six shape modes:

• Rectangular Prism — Length, width, and height (boxes, rooms, shipping containers)
• Cylinder — Radius and height (pipes, tanks, cans)
• Cone — Radius and height (funnels, piles, traffic cones)
• Sphere — Radius only (balls, domes, planets)
• Square Pyramid — Base side and height (rooftops, monuments)
• Hemisphere — Radius only (bowls, igloo shapes)

How to Use This Calculator

1. Select a shape using the buttons at the top
2. Enter your measurements in the input fields (all values must be positive)
3. See the volume immediately with a full step-by-step breakdown

Every calculation shows the formula, substitution, and arithmetic so you can learn the method while getting your answer.

Volume Formulas Explained

Rectangular prism is the simplest volume calculation. Multiply all three dimensions together: $V = l \times w \times h$. This is the same formula you use for any box-shaped object.

Cylinder volume builds on the area of a circle. You find the area of the circular base ($\pi r^2$) and then multiply by the height: $V = \pi r^2 h$. This works for any shape with a uniform circular cross-section.

Cone volume is exactly one-third of a cylinder with the same base and height: $V = \frac{1}{3} \pi r^2 h$. The factor of one-third appears because a cone tapers to a point.

Sphere volume uses the formula $V = \frac{4}{3} \pi r^3$. The radius is cubed because volume is a three-dimensional measurement.

Square pyramid volume follows the same one-third rule as a cone. The base area is the side length squared, so: $V = \frac{1}{3} s^2 h$.

Hemisphere is exactly half of a sphere: $V = \frac{2}{3} \pi r^3$. This comes from dividing the sphere formula by 2.

When You’ll Need Volume Calculations

Volume shows up constantly in practical and professional situations:

• Concrete and fill material — Ordering concrete, gravel, or mulch requires knowing the volume of the space to fill. Under-ordering means a second delivery; over-ordering means wasted material and money.
• Water tanks and pools — Sizing a water tank, calculating pool capacity, or determining how long it takes to fill or drain a container all require volume. A cylindrical tank with a 3-foot radius and 8-foot height holds about 226 cubic feet of water.
• HVAC and airflow — Heating and cooling calculations start with the volume of air in a room. A 12 by 15 foot room with 8-foot ceilings contains 1,440 cubic feet of air that needs to be conditioned.
• Shipping and storage — Figuring out whether items fit inside a container, truck, or storage unit comes down to comparing volumes. Irregular shapes can be approximated by combining prisms and cylinders.
• Landscaping — Calculating how many cubic yards of topsoil, mulch, or sand to order for a garden bed. A bed that is 10 feet long, 4 feet wide, and 6 inches deep needs about 0.74 cubic yards of material.
• Cooking and baking — Scaling recipes between different pan sizes requires comparing volumes. A 9-inch round pan and an 8-inch square pan hold different amounts of batter despite similar-sounding dimensions.

Tips for Accurate Results

Use consistent units. If your length is in feet, make sure width and height are also in feet. The result will be in cubic feet. Mixing inches and feet produces incorrect answers.

Convert when needed. There are 27 cubic feet in one cubic yard and 1,728 cubic inches in one cubic foot. Concrete is typically sold by the cubic yard, so divide your cubic-foot result by 27.

Round up for materials. When ordering concrete, mulch, or fill, always round up to the next whole unit. Running short on a job site is far more expensive than having a small surplus.

Related

Want to learn more about the geometry behind these formulas? Explore our Geometry topics for detailed explanations with worked examples and practice problems.