Angle Converter

Free Online Angle Converter

This angle converter instantly converts between degrees (°), radians (rad), gradians (grad), arcminutes ('), arcseconds ("), and turns (full revolutions). It works as a degrees to radians converter, radians to degrees converter, gradians to degrees converter, degrees to gradians calculator, and arcminutes to degrees converter all in one tool, so you never need to remember individual conversion formulas or search for a separate calculator for each unit pair.

Whether you're a student solving trigonometry or geometry homework, an engineer working with radians in calculus and physics equations, a surveyor or navigator using gradians and arcminutes for precise measurements, a game developer converting rotation values between degrees and radians for code, or a machinist reading angular tolerances in arcseconds, this angle conversion calculator gives you an instant, accurate result along with a visual diagram and complete step-by-step working.

How to Use This Angle Conversion Calculator

Using this online angle converter takes only three quick steps. Enter the numeric value you want to convert, choose the unit you're converting from in the "From" dropdown, and choose the unit you want to convert to in the "To" dropdown — the converted result updates instantly as you type. Use the swap button to instantly reverse the conversion direction, or tap one of the popular conversion shortcuts like degrees to radians, radians to degrees, or degrees to gradians.

• Type the angle value you want to convert
• Select the unit you're converting from (degrees, radians, gradians, arcminutes, arcseconds, or turns)
• Select the unit you want to convert to
• Read the converted angle, the unit rate, and the visual conversion diagram

Angle Conversion Formula

Every angle conversion uses the degree as a common base unit, since degrees are the most widely recognized unit for measuring angles. To convert any value from one unit to another, the calculator first multiplies the input by that unit's degree factor to get the angle in degrees, then divides by the target unit's degree factor to reach the final answer. This two-step method solves any equation you enter — just type a value and both units, and it computes automatically.

• Step 1: Angle in degrees = Input value × (degree factor of the "From" unit)
• Step 2: Result = Angle in degrees ÷ (degree factor of the "To" unit)
• Combined formula: Result = Input value × (From unit's degree factor ÷ To unit's degree factor)
• Example shortcut: to convert degrees directly to radians, multiply by π ÷ 180 ≈ 0.0174533

Common Angle Conversion Factors

These are the exact degree-based conversion factors this calculator uses internally. Knowing them is useful for quick mental estimates even when you don't have the calculator open:

• 1 degree (°) = 1 degree (the base unit)
• 1 radian (rad) = 57.29578 degrees = 180/π degrees
• 1 gradian (grad) = 0.9 degrees (also called a "gon")
• 1 arcminute (') = 0.0166667 degrees = 1/60 of a degree
• 1 arcsecond (") = 0.0002778 degrees = 1/3600 of a degree
• 1 turn (full revolution) = 360 degrees = 2π radians
• 1 degree ≈ 0.0174533 radians (π ÷ 180)

Worked Example: Degrees to Radians

Suppose you want to convert a 90-degree right angle into radians. First, look up the conversion factor: 1 degree equals exactly 1 degree, and 1 radian equals 57.29578 degrees. Converting via degrees, 90° × 1 = 90 degrees, then 90° ÷ 57.29578 = 1.5708 radians (which is exactly π/2). So 90 degrees equals about 1.5708 radians — exactly what the diagram above shows when you enter 90 in the "From: Degree" field and select "To: Radian".

Now try a reverse example: converting 200 gradians into degrees. Since 1 gradian equals 0.9 degrees, you simply multiply: 200 grad × 0.9 = 180 degrees, a straight angle. This two-step "convert to the base unit, then convert out" method is exactly what powers every conversion this calculator performs, no matter which two angle units you enter into the equation.

Degrees, Radians, Gradians, and Other Angle Units

Degrees are the everyday unit for angles, dividing a full circle into 360 equal parts, and are used in navigation, geography, construction, and general education. Radians are the standard unit in mathematics, physics, and engineering because they relate an angle directly to the arc length of a circle, which makes calculus formulas involving sine, cosine, and rotational motion much simpler.

Gradians (also called gons) divide a full circle into 400 equal parts and are still used in some surveying and civil engineering contexts across Europe. Arcminutes and arcseconds subdivide a single degree into 60 and 3,600 parts respectively, and are used in astronomy, navigation, and precision optics where extremely small angular differences matter. A turn, or full revolution, simply represents one complete rotation of 360 degrees, often used in engineering and mechanics to describe rotational count.

Where Angle Conversion Is Used

Angle conversion comes up constantly outside the classroom, in situations where angular measurements from different systems need to be compared or combined:

• Mathematics and physics, converting between degrees and radians for trigonometric functions and calculus
• Programming and game development, converting rotation values between degrees and radians for graphics and animation code
• Surveying and civil engineering, working with gradians and arcminutes for land measurement
• Astronomy and navigation, using arcminutes and arcseconds to describe precise celestial or positional angles
• Mechanical engineering, converting turns and degrees to describe rotational movement of gears and shafts
• Architecture and construction, converting angles between degrees and gradians across different regional standards