How this calculator works
The same triangular cross-section runs along the whole prism, so multiply its area by the perpendicular prism length. Right-leg and base-height modes halve a product. SSS uses Heron area, SAS uses the sine of the included angle and ASA uses the law of sines before finding area. Reverse modes divide the volume by the known area or length.
Formula
V=KL; L=V/K; K=V/L. K=bh/2 or ab sin C/2; for SSS, K=√[s(s-a)(s-b)(s-c)] with s=(a+b+c)/2. For ASA, A=π-B-C and b=a sin B/sin A.
Worked example
A 3-4-5 triangular end has area 6 m². A perpendicular prism length of 10 m gives volume 60 m³. A 5-12-13 end has area 30 m², so a 210 m³ prism has length 7 m.
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Frequently asked questions
Which height belongs in base-height mode?
The perpendicular height inside the triangular end. The length of the prism is a separate input.
Can I use a sloping edge as prism length?
For a right prism it equals the perpendicular separation. For an oblique prism, enter perpendicular separation rather than the sloping lateral edge.
Can volume determine the whole triangle?
No. Volume and prism length determine its area, but many different triangles share that area.