Right Triangle Tool
Find missing right-triangle sides, acute angles, area, perimeter and circle radii from seven supported input combinations. View a proportional diagram, side comparison chart and formula breakdown, then export measurements or the diagram without a server.
| Measurement | Value |
|---|
The longest side is always the hypotenuse.
Table of Contents
Highlights
- Seven flexible right-triangle input combinations
- Interactive, proportionally scaled triangle diagram
- Sides, angles, area and perimeter at a glance
- Altitudes, semiperimeter and circle radii included
- Precision control and CSV, JSON, SVG or PNG exports
How Right Triangle Tool Works?
A right triangle has two perpendicular legs a and b, a hypotenuse c, and a right angle at C. Angle A is opposite leg a, while angle B is opposite leg b. The Pythagorean theorem determines the hypotenuse from both legs:
If a hypotenuse and one leg are known, the other leg follows from the same identity. With one acute angle and a side, sine, cosine or tangent determines the remaining sides. The angles obey A + B = 90°. Area and perimeter also provide ways to reconstruct the two legs.
| Known values | Relationship used |
|---|---|
| Legs a and b | c = √(a² + b²) |
| Hypotenuse c and leg a | b = √(c² − a²), with c > a |
| Hypotenuse c and angle A | a = c sin A; b = c cos A |
| Leg a and angle A | b = a / tan A |
| Area K and leg a | b = 2K / a |
| Perimeter P and leg a | b = ((P − a)² − a²) / (2(P − a)) |
The same angle relationships can use B or leg b instead. The tool accepts seven input selections: both legs; hypotenuse and one leg; one leg and an acute angle; hypotenuse and an acute angle; acute angle and other leg; area and one leg; or perimeter and one leg. Users can specify which leg and angle are referenced.
Additional measurements include the altitude to the hypotenuse h = ab/c, semiperimeter s = P/2, inradius r = (a + b − c)/2, and circumradius R = c/2. Results appear in a table, a proportionally scaled triangle drawing, side-length bars and a formula breakdown. The length labels support mm, cm, m, km, in, ft and yd; angles are in degrees. Display precision ranges from 0 to 8 decimal places, with CSV, JSON, SVG, PNG and summary-copy export options.
Practical Use Cases
Carpenters: Check the diagonal of a rectangular frame by entering its two perpendicular edges, then compare the hypotenuse with the planned brace.
Roof designers: Enter a horizontal run and roof angle to estimate a sloping rafter length, the corresponding rise and the acute angles of the section.
Surveyors: Use a horizontal offset and observed acute angle to calculate a perpendicular distance in a right-triangle layout.
Students: Explore how different known measurements reconstruct the same triangle, and compare the geometry with the Pythagorean and trigonometric formulas.
Graphic designers: Work out the diagonal, area and proportions of a right-angled composition, while viewing the scaled shape and side comparisons.
Accuracy and Limitations
The results use JavaScript floating-point arithmetic, so they are approximate, not exact symbolic values; displayed figures are rounded to the selected 0–8 decimal places. Inputs must be finite and positive, acute angles strictly between 0° and 90°, and the hypotenuse longer than the supplied leg. The solver rejects triangles with leg ratios below 10−14 in either direction. The drawing preserves proportions but is not a dimensioned engineering plan; extremely small features and angle labels may be difficult to see. The tool assumes a flat Euclidean right triangle and does not account for measurement uncertainty.
