Oblique Triangle Calculator
Solve any oblique (non-right-angle) triangle. Enter three known elements — any mix of sides and angles — and the calculator finds all remaining sides, angles, area, perimeter, inradius and circumradius using the law of cosines and law of sines.
Known elements
Area = ½ · a · b · sin C
- 1
Angle C
33.557° - 2
sin C
sin(33.557°) = 0.5528 - 3
½ × a × b
½ × 7 × 9 = 31.5 - 4
Area = ½ · a · b · sin C
31.5 × 0.5528 = 17.4123
How does this calculator work?
An oblique triangle (no right angle) is solved using: Law of cosines (c² = a²+b²−2ab cos C) for SSS and SAS cases; Law of sines (a/sin A = b/sin B = c/sin C) for AAS and SSA. Area = ½ab sin C; inradius r = Area/s; circumradius R = abc/(4·Area). All four standard input combinations are supported.
Formula
How this is calculated
An oblique triangle is any triangle that contains no 90° angle. Solving it means finding all three sides and all three angles when at least three independent measurements are known. There are four standard configurations: SSS (three sides), SAS (two sides and the included angle), AAS (two angles and a non-included side) and SSA (two sides and an opposite angle, which can occasionally give two solutions — this calculator returns the first).
For SSS and SAS the law of cosines is applied first (c² = a² + b² − 2ab cos C), and the remaining angles follow from further applications of the law of cosines or the law of sines. For AAS, the third angle is found from the 180° angle sum, then the remaining sides from the law of sines (a/sin A = b/sin B = c/sin C). SSA is the "ambiguous case" — sinB = b sin A / a may have zero, one or two solutions; this calculator returns the acute-angle solution when two exist.
From the fully solved triangle the area is ½ab sin C, the semi-perimeter is s = (a+b+c)/2, the inradius is r = Area/s (the radius of the inscribed circle), and the circumradius is R = abc/(4 Area) (the radius of the circumscribed circle). All angles are in degrees and any consistent length unit may be used for the sides.
Frequently asked questions
Any triangle that has no right (90°) angle — it may be acute (all angles < 90°) or obtuse (one angle > 90°). Solving oblique triangles uses the law of cosines and law of sines rather than the Pythagorean theorem.
When you know two sides and an angle that is not between them (SSA), there may be 0, 1 or 2 valid triangles. This happens because the given side opposite the angle could swing to two positions. The calculator returns the first (acute-angle) solution if two exist.
Yes. The three interior angles of every triangle sum to 180°. The calculator derives the third angle from this identity whenever two angles are given and checks the constraint on all outputs.
Also known as
TG we-Calculate Editorial Team. (2026). Oblique Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/oblique-triangle-calculator
TG we-Calculate Editorial Team. "Oblique Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/oblique-triangle-calculator.
TG we-Calculate Editorial Team, "Oblique Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/oblique-triangle-calculator
@misc{wecalculate_oblique_triangle_calculator, title = {Oblique Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/oblique-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?