Triangular Prism Calculator
Compute triangular prism volume, surface area, base perimeter, and lateral area from dimensions, units, and density with render-ready formulas.
Equation Preview
Helping Notes
Modes follow the Omni tool: base-height, right triangle, SSS, SAS, ASA, or base area. L is always needed for volume.
Surface area needs triangle perimeter; it’s unavailable in modes where only base+height or just area is given. :contentReference[oaicite:2]{index=2}
Angles use degrees. Units are consistent—use the same units for all sides and L for coherent results.
Results
Base Area
Surface Area
Volume
What Is a Triangular Prism Calculator?
A Triangular Prism Calculator estimates geometric properties of a prism whose bases are congruent triangles and whose faces are rectangles. It focuses on the essentials a builder, student, or engineer needs: base triangle area, prism volume, lateral surface area, total surface area, and base perimeter. You can enter dimensions in familiar units (inches, feet, centimeters, meters) and the tool standardizes them to compute correct results. The calculator supports several ways to describe the base—using base and height, three sides (Heron’s method), or an equilateral shortcut—then multiplies by the prism length. Results help with material takeoffs (e.g., sheet coverage), container capacity, and education. When density is provided, the calculator can also estimate mass by multiplying density by volume for quick planning or comparisons.
About the Triangular Prism Calculator
The prism may be right (length is perpendicular to the triangular base) or oblique; volume is the same either way because it depends only on base area and length. Surface calculations separate the lateral area from the total surface area so you can budget coverings or paint. For triangle inputs, you can supply base and height or three sides . The engine then evaluates formulas like or with . After computing , volume follows as , lateral area as , and total area as , where is the base perimeter.
How to Use This Triangular Prism Calculator
- Choose your base description: (a) base and height; (b) three sides; or (c) equilateral side length.
- Enter prism length (sometimes called height or depth) and select units. Optional: enter material density to estimate mass.
- Submit to compute: base area, perimeter, volume, lateral area, and total surface area. Review unit-consistent outputs.
- For materials planning, round up to supplier increments and include waste/overlap according to project practice.
Examples
- Right 3–4–5 triangle, L = 10: , , , , .
- Heron case a=7, b=8, c=9, L = 20: , , , , , .
- Equilateral base a=5, L = 15: , , , , .
Formula Snippets Ready for Rendering
FAQs
What inputs do I need for the base triangle?
Either base and height, three sides (for Heron’s formula), or a single side if the triangle is equilateral.
Is this for right prisms only?
No. Volume uses base area times length and works for right or oblique prisms. Surface formulas use base perimeter and length.
Can I mix units like inches for sides and feet for length?
Yes. The calculator standardizes units internally before applying formulas to ensure consistent, correct results.
How do I find triangle height if I only know sides?
Use Heron’s formula to get base area, then compute height as h = 2A / b if you need it for documentation.
What’s the difference between lateral and total surface area?
Lateral excludes the two triangular bases; total surface area includes both bases plus all rectangular side faces.
Can it estimate weight?
Yes, if you supply material density. Multiply density by volume to get mass or weight (adjusting for units and gravity).
Are the examples rounded?
Yes. Displayed values are rounded for readability. Your calculator can show more precision if you need exactness.
What if the triangle is obtuse?
Heron’s formula handles any valid triangle—acute, right, or obtuse—so the base area and downstream results remain correct.
Why do I need perimeter?
Perimeter multiplied by length gives lateral area, which is essential when estimating cladding, wraps, or paint coverage.
How precise should my measurements be?
Match precision to your project. More exact inputs yield more reliable volumes and surface areas, reducing material waste.
Can I calculate from coordinates?
Yes—convert coordinates to side lengths first (distance formula), then use the same base-area and perimeter equations.
Does orientation change the result?
No. Rotating or translating the prism doesn’t affect volume or surface measures as long as dimensions remain the same.
Will this work for hollow prisms?
Compute outer and inner volumes separately and subtract. For surface, include both inner and outer lateral areas as needed.
How do I handle unit conversions?
Enter your preferred units; the tool converts to a consistent system before calculation and converts outputs back if desired.
What common mistakes should I avoid?
Mixing units inadvertently, swapping base and height, or entering sides that cannot form a triangle (violating triangle inequality).