MyTrigCalculator.com

Right Triangle Calculator

Calculate all angles, sides, area, and perimeter of any right triangle. Enter any two known values and instantly get complete solutions with step-by-step explanations and visual diagrams.

Enter Known Values

Sides

Angles

Results

Reference Guide

B = 3 A = 4 C = 5 A ~ 53deg B ~ 37deg 90deg

Example: 3-4-5 right triangle

Enter any known values above to calculate the rest

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

a b c

a² + b² = c²

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. For a deeper dive into this concept, see the Khan Academy right triangle trigonometry course. Enter any two sides in the calculator above to find the third!

Triangle Area

base height

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

θ α

sin θ = opp/hyp

cos θ = adj/hyp

tan θ = opp/adj

Trigonometric functions help find angles from sides. Learn more about finding angles in right triangles at Math is Fun. 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

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Deepen your understanding of right triangles and trigonometry with our guides and tutorials:

Understanding Trigonometry

The math behind every structure, screen, and signal

Trigonometry is one of those rare branches of mathematics that touches nearly every part of modern life — from the phone in your pocket to the roof over your head. At its core, trigonometry studies the relationships between the angles and sides of triangles. That might sound abstract, but these relationships govern how engineers design bridges, how GPS satellites pinpoint your location, how video game characters move across a screen, and how electricians calculate voltage in alternating current circuits.

The word itself comes from the Greek trigonon (triangle) and metron (measure). People have been measuring triangles for over 4,000 years — Babylonian astronomers used triangle ratios to track celestial movements around 1800 BCE, and Egyptian builders relied on the famous 3-4-5 triangle to ensure their monuments rose perfectly square. Today, the same principles power everything from robotic arm movement to music synthesis algorithms.

This site exists to make those calculations fast, accurate, and educational. Every calculator on MyTrigCalculator.com is built to do more than spit out a number — it's designed to help you understand the math behind the result. Whether you're a student working through homework, a carpenter squaring up floor joists, or an engineer verifying load calculations, the goal is the same: give you the answer and show you why it works.

Sine, Cosine & Tangent

θ Opposite Adjacent Hypotenuse

SOH — CAH — TOA

sin θ

Opp / Hyp

cos θ

Adj / Hyp

tan θ

Opp / Adj

Every trigonometric calculation ultimately rests on three fundamental functions — sine, cosine, and tangent. These functions define the ratio between specific sides of a right triangle relative to a given angle.

These aren't just textbook definitions. When a surveyor aims a theodolite at the top of a building and reads a 32° angle of elevation from 50 meters away, it's the tangent function that converts that angle into the building's height: height = 50 × tan(32°) = 31.24 meters.

The three functions also have reciprocal counterparts — cosecant (csc), secant (sec), and cotangent (cot). What makes these functions powerful is their universality. The sine of 30° is always exactly 0.5, regardless of how large or small the triangle is. This consistency is what allows architects to work from blueprints and engineers to model structures in software before building them in steel.

The Unit Circle

θ sin θ cos θ r = 1 x y (cos θ, sin θ)

The unit circle is a circle with a radius of exactly 1, centered at the origin of a coordinate plane. It's the conceptual bridge that extends trigonometry beyond right triangles into the full 360° rotation — and eventually into the wave functions that describe sound, light, electricity, and quantum mechanics.

Place a right triangle inside the unit circle so that the hypotenuse is the radius (length 1). In this configuration, the cosine of the angle equals the x-coordinate and the sine equals the y-coordinate. As the angle rotates from 0° to 360°, these coordinates trace out the familiar sine and cosine wave patterns.

This is why trigonometry appears in fields that seem to have nothing to do with triangles. Alternating current follows a sine wave. Sound waves are combinations of sine waves. Computer graphics engines use unit circle math to rotate objects and simulate camera movement.

The most commonly referenced angles are 0°, 30°, 45°, 60°, and 90°. Master these reference angles and you can solve most standard trigonometry problems without a calculator.

Real-World Applications

From construction sites to outer space

Construction & Architecture

Every roof rafter and staircase is a right triangle problem. Roof pitch, stair stringers, and the 3-4-5 method for squaring corners all rely on trig.

Engineering & Physics

Force vectors decompose into components using sine and cosine. A cable at 40° supporting 500 lbs needs 500 ÷ sin(40°) = 777.9 lbs of tension.

Navigation & GPS

GPS relies on trilateration — solving spherical triangles to calculate position. Navigation still uses bearings rooted in trig.

Games & Computer Graphics

3D engines perform millions of trig operations per second for line-of-sight, camera rotation, and ray tracing. Trig brings video games to life.

Astronomy & Space

Trigonometric parallax has mapped nearly two billion stars. NASA uses trig for orbital trajectories and antenna pointing for deep space communication.

DIY & Home Improvement

Ladder safety angles, deck layouts, and fence grades all come down to right triangle math you can solve in seconds.

The Right Triangle

a = 3 b = 4 c = 5 a² + b² = c² 9 + 16 = 25

Everything in trigonometry connects back to the right triangle — a triangle containing one 90° angle. The Pythagorean theorem (a² + b² = c²) governs the relationship between its sides and remains the most widely used formula in applied mathematics.

Knowing any two measurements (two sides, or one side and one angle) is enough to determine everything else — all three sides, all three angles, the area, and the perimeter. This is the principle behind every calculator on this site.

Non-right triangles use extensions of the same principles. The Law of Sines and Law of Cosines together can solve any triangle — making them indispensable in surveying, navigation, and structural analysis.

Common Trig Formulas

Formula Expression Use case
Pythagorean a² + b² = c² Third side of a right triangle
Sine sin(θ) = opp / hyp Heights, vertical components
Cosine cos(θ) = adj / hyp Distances, projections
Tangent tan(θ) = opp / adj Slopes, elevation angles
Law of Sines a/sin A = b/sin B Non-right triangles (AAS, ASA)
Law of Cosines c² = a² + b² − 2ab cos C Non-right triangles (SAS, SSS)
Area (base-height) A = ½ × b × h When height is known
Area (SAS) A = ½ ab sin C Two sides + included angle
Heron's formula √[s(s−a)(s−b)(s−c)] All three sides known
Deg → Rad rad = deg × π / 180 Converting angle units

Why Accuracy Matters

All calculators on MyTrigCalculator.com perform computations using IEEE 754 double-precision floating-point arithmetic — the same standard used by scientific computing software, engineering applications, and financial systems. This provides approximately 15–17 significant decimal digits of precision, which exceeds the requirements of virtually any practical application.

The calculators also include construction-specific features like feet-and-inches mode with fractional inch precision down to 1/16" — a feature built from real-world experience on job sites where decimal feet are impractical and tape measures read in fractions.

Every calculation runs entirely in your browser. No data is sent to any server, no inputs are stored, and no personal information is collected. The site uses Plausible Analytics — a privacy-friendly, cookieless analytics platform — so there are no tracking cookies to worry about.