How this calculator works
For side ratios, divide the perimeter among the three terms and check the triangle inequality. For angle ratios, divide 180 degrees among the terms first. The sine rule then gives a proportional set of sides, which is scaled to the requested perimeter. Side shares generally differ from angle shares. The output table makes this difference visible and helps prevent treating a 1:2:3 angle ratio as a 1:2:3 side ratio.
Formula
Side ratios p:q:r give a = Pp/(p+q+r), and similarly b and c. Angle ratios give A = πp/(p+q+r). Then a:b:c = sin A:sin B:sin C.
Worked example
Side ratio 3:4:5 with perimeter 24 m gives sides 6 m, 8 m and 10 m. Angle ratio 1:2:3 gives angles 30°, 60° and 90°, whose sides are in ratio 1:√3:2.
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Frequently asked questions
Can any three positive side terms form a triangle?
No. The two smaller terms must add to more than the largest. The ratio 1:2:3 would make a flat outline and is rejected.
Do angle ratios need the triangle inequality?
No. Three positive angle terms are scaled to sum to 180 degrees. The side lengths are then derived from their sines.
Does doubling every ratio term change the answer?
No. Only the relative proportions matter. A common multiplier cancels during normalisation.