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Triangle calculator
Type any three measurements onto the figure — angles, sides or a mix — and the triangle redraws itself with everything the three of them determine. Where they determine nothing, it stays blank instead of guessing.
How to use it
- Click a box on the drawing and type a value. Angles are in degrees; sides can be in any unit you like, as long as you use the same one throughout.
- After three values the triangle is fixed and the other boxes fill in. Two of them can be angles — the third angle is always 180° minus the other two, so it carries nothing new.
- Type a fourth value and the oldest is released to make room, with an undo button. That way the drawing is always a real triangle rather than a contradiction.
- If two triangles fit your numbers, both are drawn and you can switch between them.
Three measurements, and why one of them has to be a length
A triangle is pinned down by exactly three independent measurements, which is why this tool asks for three and then stops. The catch is that the three angles are not independent of each other: they always add to 180°, so once you know two the third is fixed and tells you nothing further. Three angles therefore give you a shape without a size — every triangle with those angles, from one you could draw on a stamp to one spanning a field, fits equally well. The tool says so directly: with three angles it draws the correct shape and shows the sides as a ratio rather than pretending to know a length.
That is also why at least one of your three values has to be a side. A single length is what turns a shape into a triangle of a particular size, and from that one length the law of sines gives you the other two immediately.
The case where two different triangles are correct
If you give two sides and an angle that is not between them — the arrangement usually written SSA — your numbers can describe two genuinely different triangles. The reason is easy to see on the drawing: swinging the known side down from its corner like a compass arm can cross the opposite line at two separate points, and each crossing is a valid triangle. Most calculators quietly return the acute one and say nothing, which is how a student loses marks for an answer they were told was right.
This tool draws both, one solid and one dashed, with the swung arc that produces them, and lets you switch between the two sets of numbers. It also refuses the trap in the other direction. The rule most people memorise — that two triangles exist whenever the opposite side lands between the height and the adjacent side — is only true when the given angle is acute. At 120° with an adjacent side of 10 and an opposite side of 9 that rule says two, and the honest answer is none: the side facing the largest angle has to be the longest.
What it will not do
It will not invent a number. Two values, or three that happen to leave the triangle free, produce blank boxes and a line telling you what is still missing, because a plausible-looking answer in the right box is worse than an empty one. Measurements that no triangle can have — sides of 1, 2 and 10, say — get the arithmetic that rules them out rather than the word "invalid": two sides have to be longer together than the third, and 1 + 2 does not reach 10.
It has no unit selector, deliberately. A triangle is scale-invariant, so the answers are the same whether your sides are millimetres or miles as long as you are consistent, and a unit dropdown would only add a way to convert your own numbers by accident.
Questions
Why did my fourth value clear one of the others?
Because three measurements already fix a triangle, so a fourth can only ever agree with them or contradict them. Rather than making you delete something before you can change your mind, the oldest value is released and the box you just typed in takes its place — with an undo button if that was not what you wanted. The same applies to the third angle you type: angles come in a set that always adds to 180°, so only two of them can ever be independent.
I typed three angles and the sides came out as decimals like 1 : 0.684 : 0.347. Why not real lengths?
Because there are none to give. Three angles fix the shape of a triangle and nothing about its size — a tiny one and an enormous one with the same angles are both correct. What the tool can honestly tell you is the ratio between the sides, which is what those numbers are. Type any one real length into a side box and all three become lengths immediately.
Which formula does it use?
Whichever the arrangement calls for: the angle sum for a missing third angle, the law of sines when you have an angle and the side facing it, and the law of cosines for three sides or for two sides with the angle between them. The worked lines under the figure name the one used and show your numbers substituted into it. Internally some of them are evaluated in a rearranged but algebraically identical form that keeps more precision on very thin triangles — the printed formula is the one you would check by hand.
Are the angles in degrees or radians?
Degrees. A right angle is 90, and the three angles of your triangle always add to 180.
Can I use it for a right triangle?
Yes — type 90 into one of the angle boxes and give any two other measurements. The corner is then marked with a square instead of an arc. Pythagoras is the special case where you know the two shorter sides: type them in and the hypotenuse appears.
Does anything I type leave my browser?
No. The whole calculation is a few dozen lines of arithmetic running on this page, and there is no server involved at any point. Nothing is uploaded, stored or logged.
Updated 2026-08-20. Runs fully in your browser — nothing is uploaded.