Angle Converter
Convert between degrees, radians, gradians, arc minutes, arc seconds, and more. Free, fast, and accurate angle conversions for math, engineering, and navigation.
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How to Use
- 1 Enter your angle value in the input field. You can enter any number, including negative values and decimals (e.g., 90, 3.14159, -45).
- 2 Select your source unit from the "From" dropdown. Choose from 8 angle units including degrees, radians, gradians, arc minutes, arc seconds, turns, quadrants, and sextants.
- 3 Select your target unit from the "To" dropdown. Use the swap button to quickly reverse the conversion direction.
- 4 View your results instantly with pi notation for radians (e.g., π/2), angle type classification (acute, right, obtuse), and common equivalents.
Pro Tip: When converting to radians, common angles like 30°, 45°, 60°, 90° will show their pi notation (π/6, π/4, π/3, π/2) for easy reference in mathematical formulas.
Frequently Asked Questions
How do I convert degrees to radians?
To convert degrees to radians, multiply by π/180. For example, 90° = 90 × (π/180) = π/2 radians ≈ 1.5708. Our converter handles this automatically - just enter the degrees and select radians as the target unit. The formula is: radians = degrees × (π/180).
How do I convert radians to degrees?
To convert radians to degrees, multiply by 180/π. For example, π radians = π × (180/π) = 180°. Our converter shows the result instantly when you enter radians and select degrees. The formula is: degrees = radians × (180/π).
What is a gradian (gon)?
A gradian (also called gon or grade) is an angular unit where a right angle equals 100 gradians, making a full circle 400 gradians. This system is used in surveying because it makes calculations easier - 1 gradian = 0.9 degrees. The relationship is: 90° = 100 grad = π/2 rad.
What are arc minutes and arc seconds?
Arc minutes (′) and arc seconds (″) are subdivisions of degrees used for precise angular measurements, especially in astronomy and navigation. 1 degree = 60 arc minutes = 3,600 arc seconds. For example, the apparent diameter of the Moon is about 31 arc minutes.
What are the different angle types?
Angles are classified by their measure: Acute (0° to 90°), Right (exactly 90°), Obtuse (90° to 180°), Straight (exactly 180°), and Reflex (180° to 360°). Our converter automatically identifies the angle type based on your input.