Triangular Prism Calculator

Calculate triangular prism volume from a triangle’s base and height, or enter its three sides to find volume and surface area. View a labeled diagram and follow the calculation steps.

Calculate Your Prism

This tool calculates a right prism: its length is perpendicular to the triangular ends. The triangle itself can have any valid shape.

Triangle height is perpendicular to the base. It is not necessarily one of the triangle’s sides.

Distance between the two triangular ends. Enter all measurements in the selected input unit.

Triangular prism dimensions A triangular prism with triangle base, perpendicular triangle height and prism length labeled. h b L
Diagram is illustrative and not to scale. L is prism length; h is triangle height.

Planning a concrete pour? Use the concrete calculator to estimate material quantities for its supported shapes.

QUICK START

How to Use the Triangular Prism Calculator

Choose the triangle measurements you know, enter the prism length and follow the calculation.

  1. Choose your measurement method

    Select base and perpendicular height to calculate volume, or three sides to calculate both volume and surface area. Both methods describe the triangular end of the prism.

  2. Enter the triangle and prism lengths

    Enter positive measurements in one input unit. Triangle height is perpendicular to its base. Prism length is the distance between the two triangular ends. These are different measurements.

  3. Select result units and rounding

    Choose your result unit and two, four or six decimal places. Volume uses cubic units, such as cm³, while triangle area and surface area use squared units, such as cm².

  4. Review the working and copy

    Check the triangle area, then follow V = A × L. In three-sides mode, review the surface area too. Select Copy Result to save the displayed measurements, or Clear to start again.

Keep your measurements consistent: All input lengths use the same selected unit. Changing the input unit converts populated fields; changing the result unit converts the output. This calculator assumes a right prism, with its length perpendicular to the triangular ends.

WORKED EXAMPLES

Triangular Prism Step by Step

Find the triangle area first, then use the prism length to calculate volume or surface area.

EXAMPLE 01 · VOLUME

Calculate volume from base and height

A prism’s triangular end has a base of 8 cm and perpendicular height of 5 cm. The prism is 12 cm long.

GIVEN MEASUREMENTS
Triangle base (b)
8 cm
Triangle height (h)
5 cm
Prism length (L)
12 cm
  1. Find the area of one triangular end

    A = b × h ÷ 2

    A = 8 × 5 ÷ 2 = 20 cm²

  2. Multiply triangle area by prism length

    V = A × L

    V = 20 × 12 = 240 cm³

  3. Check the units

    cm² × cm = cm³

ANSWER Volume = 240 cm³

Base and height are enough for volume. Surface area also needs the triangle’s perimeter.

EXAMPLE 02 · SURFACE AREA

Calculate surface area from three sides

A right prism has triangular ends with sides of 3 cm, 4 cm and 5 cm. Its length is 10 cm.

GIVEN MEASUREMENTS
Triangle sides (a, b, c)
3, 4, 5 cm
Prism length (L)
10 cm
Triangle perimeter (P)
12 cm
  1. Find triangle area using Heron’s formula

    s = (3 + 4 + 5) ÷ 2 = 6 cm

    A = √[6 × (6 − 3) × (6 − 4) × (6 − 5)]

    A = √36 = 6 cm²

  2. Find the three rectangular faces’ total area

    Lateral area = P × L

    Lateral area = 12 × 10 = 120 cm²

  3. Add both triangular ends

    S = 2A + PL

    S = 2 × 6 + 120 = 132 cm²

ANSWER Total surface area = 132 cm²

The same prism has volume V = 6 × 10 = 60 cm³.

Keep volume and surface area separate

Volume measures the space inside the prism and uses cubic units. Surface area measures its outer faces and uses squared units. For total surface area, include both triangular ends. Try these measurements in the calculator .

FORMULA REFERENCE

Triangular Prism Formulas at a Glance

Volume measures the space inside a prism. Surface area measures its outer faces. The formulas below use a right triangular prism.

Triangular prism illustrating volume A L
Volume: V = A × L Triangle area × prism length · cubic units
A triangular prism net with three rectangles and two triangles A A PL
Surface area: S = 2A + PL Two triangular ends + three rectangles · squared units
A = area of one triangular end, P = triangle perimeter, L = prism length, b = triangle base and h = perpendicular triangle height. Diagrams are not to scale.
Find Formula Measurements needed
Triangle area A = bh ÷ 2 Triangle base and height
Triangle area from sides A = √[s(s − a)(s − b)(s − c)] Three sides; s = (a + b + c) ÷ 2
Triangle perimeter P = a + b + c Three triangle sides
Prism volume V = AL Triangle area and prism length
Lateral surface area PL Triangle perimeter and prism length
Total surface area S = 2A + PL Triangle area, perimeter and prism length

Triangle height and prism length are different

Triangle height h lies within the triangular face and meets its base at a right angle. Prism length L runs between the triangular ends. For a right prism, L is perpendicular to those ends.

Include every face in total surface area

The two triangular ends contribute 2A. The three rectangular faces contribute aL + bL + cL = PL. See Math Is Fun’s explanation of prism volume and surface area for more on these relationships.

Have your measurements ready? Use the triangular prism calculator to see the working in your chosen units.

PRISM CALCULATION GUIDANCE

Frequently Asked Questions

Find answers about prism dimensions, triangle measurements, volume and surface area.

How do I calculate the volume of a triangular prism?

Find the area of one triangular end, then multiply it by the perpendicular distance between the ends. For the right prism used in this calculator, that distance is its length L. With triangle base b and perpendicular height h, V = (b × h ÷ 2) × L.

What is the difference between triangle height and prism length?

Triangle height lies within a triangular end and meets its chosen base at a right angle. Prism length runs between the two triangular ends. Use triangle height to calculate the end’s area, then use prism length to calculate the volume.

Does a right triangular prism need a right-angled triangle?

No. “Right prism” means its connecting edges are perpendicular to the triangular ends, making the three lateral faces rectangles. The triangle can be right-angled, acute or obtuse, provided its measurements form a valid triangle.

Can base and triangle height determine total surface area?

In general, no. They determine the triangle area, but not its perimeter. Total surface area also depends on the three side lengths. Select three-sides mode and enter the triangle sides plus prism length to calculate it.

Why are my three triangle sides rejected?

All sides must be positive, and the sum of any two must be greater than the third. For example, 3, 4 and 5 form a triangle, but 2, 3 and 5 do not: 2 + 3 equals 5, producing a flat shape with zero area. Check that all side values use the same input unit.

What is the difference between lateral and total surface area?

Lateral surface area includes only the three rectangular faces: PL. Total surface area also includes both triangular ends: 2A + PL, where A is the area of one end and P is its perimeter.

Can this calculator handle an oblique triangular prism?

This tool assumes a right prism. An oblique prism’s volume is still triangle area multiplied by the perpendicular distance between its ends, rather than its slanted connecting edge. Its lateral faces are parallelograms, so the surface area calculation needs additional measurements.

Can I enter centimeters and get volume in cubic meters?

Yes. Select centimeters as the input unit and meters as the result unit. Enter every input length in centimeters. The calculator converts the dimensions before calculating m² and m³ results. Remember that 1 m³ = 1,000,000 cm³.

READY TO CALCULATE?

Find Your Prism’s Volume & Surface Area

Enter the triangle measurements and prism length to find volume. Choose three-sides mode for surface area, then review the steps and copy your results.

Use Triangular Prism Calculator