Triangular Prism Surface Area Calculator
Enter the three sides of the triangle and the length of the prism. The calculator validates the triangle inequality and returns the full surface area.
A triangular prism has two parallel triangular ends joined by three rectangular side faces. Total surface area is 2 × (triangle area) + (perimeter × length). The triangle's area is computed by Heron's formula so you can use any triangle.
Mix and match length units per input (mm, cm, m, km, in, ft, yd, mi) and pick the area unit you want for the result (mm², cm², m², km², in², ft², yd², mi², acres or hectares). The calculator shows the formula being used and a clear breakdown so you can sanity-check the maths and not just trust the number.
Looking for other shapes? See our Surface Area Calculator hub for the full list of 3D shapes we cover.
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What this calculator does
Computes the surface area of a triangular prism from its dimensions, using the formula SA = 2·A_tri + (a+b+c)·L, A_tri by Heron's formula. Supports all common length units on input and any area unit on output, with a worked breakdown.
Who it is for
Students, teachers, DIYers, builders, fabricators, packaging designers and anyone who needs the surface area of a triangular prism quickly and accurately.
How to use it
Enter Triangle side a, Triangle side b, Triangle side c, Prism length (L). Choose your preferred unit for each input — you can mix units freely (e.g. some in inches and others in feet). Pick the area unit for the answer (m², ft², in², cm², acres, hectares and more). The result, the formula and the breakdown appear instantly.
How the calculation works
SA = 2·A_tri + (a+b+c)·L, A_tri by Heron's formula. Triangle 3-4-5 with prism length 10 (m): A_tri = 6 m², perimeter 12 m. SA = 12 + 120 = 132 m².
Worked example
Triangle 3-4-5 with prism length 10 (m): A_tri = 6 m², perimeter 12 m. SA = 12 + 120 = 132 m².
Assumptions and limitations
- Triangle area is computed by Heron's formula, so any valid triangle works (the three sides must satisfy the triangle inequality).
- Closed solid: all faces (ends, base, sides) are included.
- Length unit conversions use exact factors (1 in = 0.0254 m, 1 ft = 0.3048 m, 1 yd = 0.9144 m, 1 mi = 1609.344 m).
- Area outputs convert from m² using exact factors squared.
Frequently asked questions
What is Heron's formula?
A_tri = √(s·(s−a)·(s−b)·(s−c)), where s = (a+b+c)/2 is the semi-perimeter. It works for any triangle without needing the height.
What if my triangle is right-angled?
Heron's formula still works. For a 3-4-5 right triangle, A_tri = 6 (you can verify with ½·base·height = ½·3·4 = 6).
What units can I use in this triangular prism calculator?
You can enter dimensions in millimetres (mm), centimetres (cm), metres (m), kilometres (km), inches (in), feet (ft), yards (yd) or miles (mi) — and you can mix units freely between fields. The result can be shown in any area unit: mm², cm², m², km², in², ft², yd², mi², acres or hectares.
How accurate is this triangular prism surface area calculator?
Calculations use the exact closed-form formula (SA = 2·A_tri + (a+b+c)·L, A_tri by Heron's formula) with full double-precision arithmetic, so the answer is as accurate as your inputs. Length conversions use exact SI/Imperial factors (1 in = 0.0254 m, 1 ft = 0.3048 m).
Is this triangular prism surface area calculator free to use?
Yes — every calculator on Korvaix is completely free, with no sign-up, no ads in the result, and no usage limit. You can run as many calculations as you need.
What is the difference between surface area and volume?
Surface area is the total area of the outside of a 3D shape, measured in square units (m², ft²). Volume is how much space the shape takes up inside, measured in cubic units (m³, ft³). Surface area is what you need for paint, packaging, heat loss and surface coatings; volume is what you need for capacity, weight and material fill.
Where else can I find surface area calculators on Korvaix?
Visit our Surface Area Calculator hub for the full list of 17 common 3D shapes. Each shape has its own dedicated page with the formula, worked example and unit-by-unit breakdown.
Related calculators
- Annulus Area Calculator — Enter the outer and inner radii. The calculator returns A = π·(R² − r²).
- Area Calculator — Pick a 2D shape — circle, square, rectangle, triangle, trapezium, parallelogram, ellipse, regular polygon, rhombus, sector, annulus or kite
- Capsule Surface Area Calculator — Enter the radius and the straight middle length. The calculator returns 4πr² for the two rounded ends plus 2πrh for the cylindrical side.
- Circle Area Calculator — Enter the radius. The calculator returns A = πr², the area of the flat disc.
- Circular Sector Area Calculator — Enter the radius and the angle in degrees. The calculator returns the sector's area: A = ½·r²·θ (with θ converted to radians).
- Cone Surface Area Calculator — Enter the base radius and height. The calculator splits the answer into the base (πr²) and the lateral surface (πr·s), where s = √(r²+h²) is
Related guides
- Surface Area Formulas for Common 3D Shapes — A clear, plain-English guide to surface area formulas for sphere, cube, cone, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid and
Sources and references
Standard geometric surface area formula. SI and Imperial unit conversions per the International System of Units (SI) and NIST.
Last updated
Last reviewed: 2026-04-21.