Prism Volume Calculator: Formula & Steps

This prism volume calculator works out the volume of any right prism when you enter the base area and the prism height, or the base dimensions and height for common shapes like rectangular, triangular, and trapezoidal prisms. You get the volume in cubic units (cm³, m³, in³, ft³) instantly, along with the formula used. Simply choose your prism type, enter the required measurements, and the calculator returns the volume.

Formula

The general formula for the volume of a prism is:

V = A_base × h

Where:

• V = volume (cubic units: m³, cm³, ft³, etc.)
• A_base = area of the base polygon (square units)
• h = height of the prism, measured perpendicular to the base (same linear unit as the base dimensions)

For specific prism types:

• Rectangular prism: V = length × width × height
• Triangular prism: V = (½ × base × triangle height) × prism height
• Trapezoidal prism: V = ((a + b) / 2 × trapezoid height) × prism height

Worked Example

Using the default values from the calculator above (rectangular prism, a = 4 m, b = 3 m, h = 5 m):

1. Base area = a × b = 4 × 3 = 12 m²
2. Volume = base area × h = 12 × 5 = 60 m³

The calculator shows 60.00 m³, matching the manual calculation.

When to Use a Prism Volume Calculator

Use this calculator whenever you need the space inside a three-dimensional object with a constant cross-section. Common real-world uses include:

• Concrete volume for a rectangular footing or slab
• Water capacity of a fish tank or swimming pool (in liters or gallons)
• Volume of a triangular roof truss or trapezoidal channel
• Shipping crate volume for freight calculations

The calculator works for any right prism—where the sides are perpendicular to the base. For oblique prisms (leaning), the formula still works if you use the perpendicular height, not the slant length.

How to Read the Result

The volume is always in cubic units. If you enter meters, you get cubic meters (m³). One cubic meter equals 1000 liters. If you enter feet, you get cubic feet (ft³); one cubic foot equals approximately 7.48 US gallons. For example, a rectangular tank 2 m long, 1 m wide, and 0.5 m tall has a volume of 1 m³, which is 1000 liters.

Common Mistakes and Unit Mix-Ups

• Mixing units – Always convert all measurements to the same unit before calculating. If the base is in meters and the height in centimeters, convert the height to meters (or vice versa) first.
• Using slant height instead of perpendicular height – For oblique prisms, the height must be measured at a right angle to the base, not along the slanted edge.
• Forgetting the ½ in triangular prisms – The base area of a triangle is ½ × base × height. Omitting the ½ is the most common error.
• Confusing base area with base length – The formula uses the area of the base polygon, not just one side length.

Limits of the Formula

The formula V = A_base × h applies only to prisms (and cylinders, which are circular prisms). It does not apply to pyramids, cones, spheres, or irregular shapes. For a pyramid, the volume is (1/3) × base area × height. Also, the formula assumes the prism is solid and fills the entire space; if the prism has hollow sections, subtract those volumes separately.

Frequently Asked Questions

How do I calculate the volume of a triangular prism?

First, find the area of the triangular base using the formula ½ × base × height of the triangle. Then multiply that area by the prism height (the distance between the two triangular faces). For example, a triangular prism with a base of 6 cm, triangle height of 4 cm, and prism height of 10 cm has a volume of (½ × 6 × 4) × 10 = 120 cm³.

What is the difference between a prism and a pyramid?

A prism has two identical, parallel bases connected by rectangular faces, so the cross-section is the same throughout. A pyramid has one base and a single apex point, with triangular faces converging at the apex. The volume formulas differ: prism = base area × height, pyramid = (1/3) × base area × height.

Can I use this calculator for a cylinder?

Yes, a cylinder is a prism with a circular base. The volume formula is V = π × r² × h, where r is the radius of the base and h is the height. If your calculator only has rectangular/triangular/trapezoidal options, you can still approximate by using the base area (πr²) and height manually.

How do I convert cubic meters to liters?

Multiply the volume in cubic meters by 1000. One cubic meter equals exactly 1000 liters. For example, 2.5 m³ = 2500 liters. Conversely, divide liters by 1000 to get cubic meters.

What if my prism has a non-standard base shape?

For any prism, the volume is always base area × height. So, calculate the area of your base polygon (using the appropriate formula for a triangle, trapezoid, hexagon, etc.), then multiply by the prism height. The calculator above works for the most common shapes, but the underlying principle is universal.

Related

• Pocket Calculator Argos: What It Is & How to Use
• Pocket Calculator Casio: How to Pick and Use One
• Pocket Calculator Font: What It Is & How to Get It

sel type | Prism type | Rectangular=1, Triangular=2, Trapezoidal=3
in a | Base length (a) | m | 4 | 0
in b | Base width/height (b) | m | 3 | 0
in h | Prism height (h) | m | 5 | 0
out volume | Volume | m³ | type == 1 ? a * b * h : type == 2 ? 0.5 * a * b * h : ((a + b) / 2) * b * h | 2