Angle Calculator
Calculate Any Angle, Side or Triangle Easily
Enter Known Values
Results
Calculation Steps
Enter at least two values and click Calculate to see the solution steps.
How to Use This Angle Calculator
This calculator helps you solve for missing sides and angles in triangles. Simply enter any two known values (sides or angles) and the calculator will determine all the remaining values.
Two Sides Known
Enter two side lengths to calculate the third side and all angles.
Example: a=3, b=4 → c=5, A=36.87°, B=53.13°, C=90°
Side and Angle Known
Enter one side and one angle to calculate the remaining sides and angles.
Example: a=5, A=30° → b=8.66, c=10, B=60°, C=90°
Two Angles Known
Enter two angles to calculate the third angle and side ratios.
Example: A=30°, B=60° → C=90° (side ratios depend on one known side)
Formulas & Why They Work
Pythagorean Theorem
This fundamental relationship applies to all right triangles. It states that the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.
Trigonometric Ratios
These ratios relate the angles of a right triangle to the lengths of its sides. They are fundamental to solving for unknown values when you have a mix of sides and angles.
Law of Sines
This law applies to all triangles (not just right triangles) and relates the sides to their opposite angles. It's particularly useful when you know two angles and one side, or two sides and a non-included angle.
Law of Cosines
This is a generalization of the Pythagorean theorem that works for any triangle. It's used when you know two sides and the included angle, or all three sides.
When Would You Use This?
🏠 Construction & Roof Pitch
Calculate roof slopes, rafter lengths, and structural angles for building projects. Determine the correct pitch for drainage and aesthetics.
📐 Surveying & Navigation
Determine distances and angles in land surveying, GPS navigation, and mapping. Calculate bearings and plot courses.
🎯 Engineering & Design
Calculate mechanical angles, structural components, and force vectors in engineering designs and architectural plans.
📚 Education & Homework
Solve geometry problems, verify solutions, and understand trigonometric relationships for math and physics courses.
🎨 Art & Design
Calculate perspectives, proportions, and angles for artistic compositions, technical drawings, and graphic designs.
🔧 DIY Projects
Determine angles for woodworking, furniture building, home renovations, and various craft projects.
Frequently Asked Questions
Yes! If you enter two angles and one side, the calculator will use the Law of Sines to determine the remaining sides and the third angle. Remember that the sum of all angles in a triangle must be 180°.
The calculator handles all types of triangles, including obtuse triangles (with one angle greater than 90°). The Law of Sines and Law of Cosines work for any triangle shape.
Invalid results usually occur when the entered values cannot form a valid triangle. This happens if:
- The sum of two angles equals or exceeds 180°
- The side lengths don't satisfy the triangle inequality theorem (the sum of any two sides must be greater than the third side)
- You've entered conflicting values that can't mathematically coexist in a triangle
Yes! Use the unit toggle to switch between degrees and radians. The calculator will automatically convert between these units as needed.
The calculator provides results with high precision (up to 10 decimal places for calculations). However, for display purposes, results are rounded to two decimal places for better readability.