Prism Surface Area Calculator
Surface area of any right prism from its base area and perimeter, or of a regular prism from the number of sides and side length.
A prism’s surface area is the total area of every face wrapped around it — two identical base faces plus a lateral surface running between them. This calculator covers four base shapes at once: rectangular (cuboid), triangular (from three side lengths), trapezoidal, and any regular polygon (square, pentagon, hexagon, or beyond). Pick your base shape and enter its own measurements directly — there’s no need to calculate the base’s area or perimeter by hand first, since the calculator does that for you from whichever shape you choose.
Every mode reports the base area, the base’s perimeter, the lateral surface area, and the total surface area, so you can see exactly how the final number was built.
Prism Surface Area Formula
Total Surface Area = 2 × Base Area + Lateral Area, where Lateral Area = Base Perimeter × Prism Length
Where:
Base Area = the area of one of the two identical end faces
Base Perimeter = the distance around the edge of the base shape
Prism Length = the distance between the two base faces (also called the prism’s height, depth, or length, depending on orientation)
This general formula works the same way regardless of the base shape — the two base faces always contribute 2 × Base Area, and the lateral surface (the rectangle-shaped sides connecting them, unrolled flat) always equals the base’s perimeter times the prism’s length. Only the base-area and base-perimeter formulas change from shape to shape, which is why this calculator lets you pick a base shape first.
Rectangular Prism (Cuboid)
Total Surface Area = 2(Length × Width + Length × Height + Width × Height)
A rectangular prism (cuboid) has three pairs of identical rectangular faces, which is why this shortcut formula skips the general base-area-plus-lateral-area approach and computes all six faces directly.
Worked Example
A box 5 ft long, 4 ft wide, and 3 ft tall: Total SA = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2 × 47 = 94 square feet.
Triangular Prism
Base Area (Heron’s formula) = √[s(s−a)(s−b)(s−c)], where s = (a + b + c) ÷ 2
Entering the base triangle’s three side lengths lets the calculator find its area with Heron’s formula, without needing a separate height measurement — useful since a triangular prism’s base triangle isn’t always a right triangle with an obvious height.
Worked Example
A triangular prism with a 3-4-5 base triangle and a 10-ft prism length: Semi-perimeter s = (3 + 4 + 5) ÷ 2 = 6, Base Area = √[6 × 3 × 2 × 1] = √36 = 6 square feet, Base Perimeter = 3 + 4 + 5 = 12 feet, Lateral Area = 12 × 10 = 120 square feet, Total SA = 2 × 6 + 120 = 132 square feet.
Trapezoidal Prism
Base Area = 0.5 × (Side a + Side b) × Trapezoid Height
Where Side a and Side b are the trapezoid’s two parallel sides, and the trapezoid height is the perpendicular distance between them (not one of the slanted leg lengths). The base perimeter adds all four sides of the trapezoid, including the two non-parallel legs.
Worked Example
A trapezoidal prism with parallel sides 6 ft and 10 ft, a trapezoid height of 4 ft, legs of 5 ft each, and a prism length of 8 ft: Base Area = 0.5 × (6 + 10) × 4 = 32 square feet, Base Perimeter = 6 + 10 + 5 + 5 = 26 feet, Lateral Area = 26 × 8 = 208 square feet, Total SA = 2 × 32 + 208 = 272 square feet.
Prisms with a Regular Polygon Base (Square, Pentagon, Hexagon…)
Base Area = (n × Side²) ÷ (4 × tan(π/n)), where n is the number of sides
This one formula covers any regular-polygon-based prism — a square prism, pentagonal prism, hexagonal prism, or beyond — simply by changing the number of sides. The base perimeter is n × Side Length.
Worked Example: A Hexagonal Prism
A hexagonal prism (n = 6) with 4-ft sides and a 10-ft prism length: Base Area = (6 × 4²) ÷ (4 × tan(30°)) ≈ 41.57 square feet, Base Perimeter = 6 × 4 = 24 feet, Lateral Area = 24 × 10 = 240 square feet, Total SA = 2 × 41.57 + 240 ≈ 323.14 square feet.
Base Area vs. Lateral Area vs. Total Surface Area
These three numbers answer different practical questions. Total surface area covers every face and is what you’d need for a material estimate that wraps the entire prism (like a fully painted or fully wrapped solid). Lateral area covers only the sides, not the two end faces — useful when the ends are left open, hidden, or covered differently, such as painting only the outer walls of a triangular-cross-section beam. Base area alone answers questions about just one end face, like the cross-sectional area of a beam or duct.
Frequently Asked Questions
What’s the difference between lateral and total surface area of a prism?
Lateral surface area covers only the sides connecting the two base faces (Base Perimeter × Prism Length). Total surface area adds the two base faces on top of that: Total SA = 2 × Base Area + Lateral Area.
How do I find a triangular prism’s surface area from its side lengths only?
Enter the base triangle’s three side lengths along with the prism length. The calculator uses Heron’s formula to find the base area from the three sides directly, without needing a separate height measurement.
Does the calculator work for a pentagonal or hexagonal prism?
Yes — use the Regular Polygon Base mode and set the number of sides to 5 for a pentagon, 6 for a hexagon, or any other whole number of 3 or more for a different regular-polygon base.