Right Triangle Calculator
Example Data Table
Use these sample values to test different calculation methods.
| Method | Known Values | Expected Main Result | Use Case |
|---|---|---|---|
| Two legs | a = 3, b = 4 | c = 5, area = 6 | Basic geometry check |
| Hypotenuse and leg | c = 13, a = 5 | b = 12 | Diagonal layout |
| Hypotenuse and angle | c = 10, A = 30° | a = 5, b = 8.6603 | Trigonometry practice |
| Area and leg | area = 24, a = 6 | b = 8, c = 10 | Area based solving |
| Perimeter and ratio | perimeter = 60, ratio 3:4 | a = 15, b = 20, c = 25 | Scaled triangle design |
Formula Used
Pythagorean theorem: c² = a² + b²
Area: Area = ½ab
Perimeter: P = a + b + c
Angles: A = atan(a ÷ b), B = 90° - A
Trigonometry: sin(A) = a ÷ c, cos(A) = b ÷ c, tan(A) = a ÷ b
Inradius: r = Area ÷ semiperimeter
Circumradius: R = c ÷ 2
Altitude to hypotenuse: h = ab ÷ c
Hypotenuse projections: p = a² ÷ c, q = b² ÷ c
How to Use This Calculator
- Select the solving method that matches your known values.
- Enter only the values required by that method.
- Use positive lengths only.
- Enter acute angles between 0 and 90 degrees.
- Choose a unit label and decimal precision.
- Press the calculate button.
- Review sides, angles, area, perimeter, and advanced measures.
- Download the CSV or PDF report if needed.
Right Triangle Calculator Guide
What This Tool Solves
A right triangle has one square corner. The side opposite that corner is the hypotenuse. It is always the longest side. The other two sides are legs. This calculator uses those facts to complete missing values. It supports side pairs, side and angle pairs, area with one leg, perimeter with a leg ratio, and altitude to the hypotenuse.
Where It Helps
The tool is helpful in many math tasks. Students can check homework. Teachers can prepare examples. Builders can estimate ramps, braces, roof slopes, diagonal runs, and layout distances. Designers can compare proportions before drawing final plans. Each result is shown with clear units and rounded values.
Main Geometry Rules
The main rule is the Pythagorean theorem. It says that a squared plus b squared equals c squared. Trigonometry adds more options. Sine compares the opposite leg with the hypotenuse. Cosine compares the adjacent leg with the hypotenuse. Tangent compares the opposite leg with the adjacent leg. These ratios make angle based solving possible.
Extra Measurements
Area is one half of the leg product. Perimeter is the sum of all sides. The inradius is based on the semiperimeter. For a right triangle, the circumradius is half of the hypotenuse. The altitude to the hypotenuse equals the leg product divided by the hypotenuse. These extra outputs make the answer more complete.
Input Tips
Use careful input values. Choose the solve method first. Then fill only the fields required by that method. Angles must be between zero and ninety degrees. Lengths must be positive. A hypotenuse must be greater than any entered leg. When a result seems wrong, check the chosen method and units.
Graph and Export
The graph gives a quick visual check. It places the right angle at the origin. One leg runs horizontally. The other leg runs vertically. The hypotenuse closes the triangle. Use the CSV export for spreadsheets. Use the PDF export for reports, class notes, or project records.
Accuracy Notes
For best accuracy, keep one unit system through the whole problem. Do not mix feet and inches unless you convert first. Increase decimal precision for small parts. Reduce precision for quick classroom work. The exported values preserve the displayed rounding, so shared results stay consistent. This improves review.
FAQs
1. What is a right triangle?
A right triangle is a triangle with one angle equal to 90 degrees. The side opposite that angle is called the hypotenuse. It is the longest side.
2. What values can this calculator find?
It can find missing sides, acute angles, area, perimeter, semiperimeter, inradius, circumradius, altitude, projections, medians, and trigonometric ratios.
3. Which side is the hypotenuse?
The hypotenuse is side c in this calculator. It is opposite the 90 degree angle. It must be longer than each leg.
4. Can I solve with one side only?
No. One side alone is not enough. You need another valid value, such as a second side, an acute angle, area, perimeter with ratio, or altitude condition.
5. Why must angles be less than 90 degrees?
A right triangle already has one 90 degree angle. The other two angles are acute. Each must be greater than 0 and less than 90 degrees.
6. What is the altitude to the hypotenuse?
It is the perpendicular distance from the right angle to the hypotenuse. It equals a multiplied by b, divided by c.
7. Does the unit affect the calculation?
The unit is used as a label. Calculations assume all entered lengths use the same unit. Convert mixed units before entering values.
8. Can I export the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable report with the calculated triangle values.