📐 Triangle Calculator
Solve triangles from sides and angles — SSS, SAS, ASA, or SSA
🔒 100% client-side processing
How to Use
- Pick the mode: Choose the tab matching what you know — SSS, SAS, ASA, or SSA
- Enter three values: Sides are unitless positive numbers; angles are in degrees
- Read the solution: All sides, all angles, area, and perimeter appear instantly
- Check the diagram: The SVG sketch is scaled to the actual side proportions
- Watch for the ambiguous case: SSA inputs can yield 0, 1, or 2 solutions — all are listed
Features
- Four input modes — SSS, SAS, ASA, and SSA, with the inputs relabeled per mode
- Ambiguous SSA handling — explicitly reports 0, 1, or 2 solutions and lists every one
- Complete solution — all three sides, all three angles in degrees, area (Heron / ½ab·sinC), and perimeter
- Scaled SVG diagram — a schematic triangle drawn to the true side proportions, computed in pure math
- Localized validation — clear errors for impossible inputs: triangle inequality, angles that sum past 180°, non-positive values
Use Cases
- Geometry homework: Check SSS/SAS/ASA/SSA triangle solutions with the ambiguous case handled correctly
- Engineering and surveying: Solve field measurements where only partial sides and angles are known
- Carpentry and DIY: Find missing lengths and angles for triangular cuts and braces
- Teaching: Demonstrate why SSA can produce zero, one, or two triangles
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Frequently Asked Questions
What do SSS, SAS, ASA, and SSA mean?
They describe which three measurements you already know: three sides (SSS), two sides and the included angle (SAS), two angles and the included side (ASA), or two sides and a non-included angle (SSA). Choose the matching tab and the calculator solves the rest.
Why can SSA have two solutions?
With two sides and a non-included angle, the known side can sometimes swing into two different positions, producing two valid triangles. This calculator reports the ambiguous case explicitly and lists both solutions instead of silently picking one.
Are angles shown in degrees or radians?
Degrees only. Enter angles in degrees (0 to 180) and all results are returned in degrees.
Why does the calculator say my sides cannot form a triangle?
Every side of a triangle must be shorter than the sum of the other two (the triangle inequality). For example, sides 1, 2, and 10 can never form a triangle, so the calculator shows a validation error instead of a meaningless result.
How is the area computed?
For three known sides the area uses Heron's formula; when an angle is known it uses ½ab·sin(C). Both are computed exactly from your inputs.