Enter any three values of a triangle, at least one of them a side, and the calculator works out the rest. It handles right, acute and obtuse triangles and shows every step with the law of sines and the law of cosines.
How the solver works and how to get the most out of it.
Side-Angle-Side (SAS). You pinned sides b and c and the angle α (at corner A) between them. Side a is calculated first.
The method changes as soon as you pin a different combination of values.
The name lists the three known values in order around the triangle. S stands for a side, A for an angle.
Three values define a triangle. The pinned values (filled blue) are the ones you set; the other three are calculated from them.
When you type or slide a value, it becomes pinned and the oldest pin is released. Tapping the pin icon on a label pins its current value the same way, without changing the triangle. A message tells you which pin was released.
Dragging a corner changes all values directly. The pins stay, and they apply again the next time you type a value.
Three angles fix the shape of a triangle but not its size: a small and a large triangle can have exactly the same angles. Besides, the angles always add up to 180°, so the third angle carries no new information. At least one side therefore always stays pinned.
This happens with Side-Side-Angle (SSA), also called the ambiguous case. The law of sines gives the sine of a missing angle, and two angles share the same sine: θ and 180° − θ. When both lead to a valid triangle, both are solutions.
The other solution is drawn as a dashed outline. Tap it, or use Triangle 1 / Triangle 2 in the Values panel, to switch. Try the "Two solutions" example to see it.
The invalid value is not applied, so the last valid triangle stays on screen.
Corners are A, B and C. Each side is named after the opposite corner with a lowercase letter: side a lies opposite A (between B and C). The angle at each corner uses the Greek letter: α at A, β at B, γ at C. So side a and angle α always face each other, which is what the law of sines relies on.
sqrt(2), √3, 3/4, 2pi/3, 2^0.5 and decimal commas like 4,5 all work.With "Snap angles" on, any angle close to a multiple of 15° (15°, 30°, 45°, 60°, 90°, …) locks onto it, and the snapped angle lights up in orange. Near two such angles at once, the corner jumps to the point where both are exact, for example 90° and 45°.
Hold Alt (Option on a Mac) to move freely, or turn "Snap angles" off. "Snap to grid" puts corners on grid points instead, which is handy for whole-number coordinates.
The Working panel shows each step with your actual numbers.
The Shape panel tags it as Right and names the hypotenuse, the side opposite the 90° angle. The diagram draws a small square in that corner instead of an arc. For right triangles the law of cosines turns into Pythagoras' theorem, since cos 90° = 0: a² = b² + c² when α = 90°.
All calculations run at full precision; the Decimals setting (in the settings row above the values) only rounds what is shown. The length unit is a label, so the numbers are the same in any unit and nothing is converted. Angles can be shown in degrees or radians (π rad = 180°).
Numbers use the Decimals setting, and the preview shows exactly what will be copied. Images come in light or dark colours. Your choices are remembered.
Yes. Next to Copy there is a Download file button for every format, and the Share & print box lets you copy a link to the current triangle, share it through your phone's share menu, or print a one-page summary with diagram, values and working. Choose "Save as PDF" in the print dialog to get a PDF.
When the calculator is shown inside another page, such as an embed or a preview, these buttons are hidden because downloads and printing are blocked there. Copying works everywhere.
Triangle Calculator starts in your browser's language if it is one of the ten supported languages, otherwise in English. Use the language menu in the top bar to switch; your choice is remembered on this device. Numbers follow the language, for example 4,5 in German and 4.5 in English.
Your last triangle and settings are kept in this browser on this device, so they are back when you return. The calculator does not send your triangle anywhere. Reset (in the settings row above the values) brings back the starting 3-4-5 right triangle.
The page address also holds the triangle, so a bookmark or a shared link reopens it exactly.