Enter Known Values
Sides
Angles
Reference Guide
Example: 3-4-5 right triangle
Enter any known values above to calculate the rest
Note: When "Feet" is selected, input values are assumed to be in feet. Fractional inches are approximated to the nearest 1/16". The ~ symbol indicates the converted display format.
How to Use This Calculator
Enter any two known values (sides or angles) of your right triangle, then click the Calculate button to compute all the remaining values. The calculator uses the Pythagorean theorem and trigonometric functions to solve for unknown sides and angles. You can also press Enter after typing a value for quick calculation.
Formulas Used:
- Pythagorean Theorem: a² + b² = c²
- Sine: sin(angle) = opposite / hypotenuse
- Cosine: cos(angle) = adjacent / hypotenuse
- Tangent: tan(angle) = opposite / adjacent
- Area: ½ × base × height
- Perimeter: a + b + c
Why Use This Calculator?
Who Benefits
- • Students learning trigonometry and geometry
- • Teachers preparing lessons and examples
- • Engineers & architects doing quick calculations
- • DIYers planning home improvement projects
- • Construction workers measuring cuts and angles
Problems Solved
- • Quick verification of manual calculations
- • Visual understanding of triangle relationships
- • Unit conversion between feet and inches
- • Finding missing sides when you know angles
- • Learning aid with step-by-step formulas
Accuracy & Methodology
Our calculator uses IEEE 754 double-precision floating-point arithmetic and standard trigonometric formulas (Pythagorean theorem, sine, cosine, tangent) to deliver accurate results. All calculations happen directly in your browser for instant feedback. Results are displayed to appropriate precision, and we recommend verification for critical professional applications.
Calculating Right Triangles
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of squares of the other two sides. Enter any two sides in the calculator above to find the third!
Triangle Area
Area = ½ × b × h
The area of a right triangle is half the product of its base and height. Our calculator automatically computes this when you enter two sides. Try it above!
Finding Angles
sin θ = opp/hyp
cos θ = adj/hyp
tan θ = opp/adj
Trigonometric functions help find angles from sides. Enter any two values in the calculator above, and it will instantly compute all angles using sine, cosine, and tangent.
Frequently Asked Questions
How do I find the hypotenuse of a right triangle?
Use the Pythagorean theorem: c = √(a² + b²). Enter the two legs (sides a and b) in our calculator, and it will calculate the hypotenuse (side c) automatically.
What is the relationship between the angles in a right triangle?
The three angles in any triangle always sum to 180°. Since a right triangle has one 90° angle, the other two angles must sum to 90°. These are called complementary angles.
How do I calculate the area of a right triangle?
The area of a right triangle is: Area = (1/2) × base × height. For right triangles, the two legs serve as the base and height, making the formula: Area = (1/2) × a × b.
How accurate are the calculations?
Our calculator uses IEEE 754 double-precision floating-point arithmetic, which provides approximately 15-17 significant decimal digits of precision. Results are rounded to a practical number of decimal places for display. While highly accurate for educational and most practical purposes, we recommend verifying calculations for mission-critical professional applications.
Can I use this for professional or construction work?
Yes! This calculator was built by someone with over a decade of experience using trigonometry in the construction field. It's great for quick calculations, verifying measurements, and planning cuts. However, for critical structural work or engineering applications, we recommend double-checking results with professional tools or a licensed professional.
What formulas does the calculator use?
The calculator uses these standard trigonometric formulas:
- Pythagorean Theorem: a² + b² = c² (finding sides)
- Inverse Tangent: angle = arctan(opposite/adjacent)
- Sine/Cosine: Used to find sides when an angle is known
- Area: ½ × base × height
- Perimeter: Sum of all three sides
Do you store my input data?
No. All calculations are performed directly in your web browser using JavaScript. The values you enter never leave your device—nothing is sent to our servers. We use privacy-friendly analytics (Plausible) that doesn't track individual users or collect personal data. Your calculations are completely private.
How do I calculate with feet and inches?
Use the unit selector dropdown in the Results panel. Select "Feet" to see results displayed in feet and fractional inches (e.g., 5' 3-1/2"). When Feet is selected, enter your values in decimal feet (e.g., 5.5 for 5'6"). The calculator will convert results to feet and inches automatically, approximating to the nearest 1/16" for practical use.
Learn More About Trigonometry
View all articlesDeepen your understanding of right triangles and trigonometry with our guides and tutorials: