Radians to Degrees Calculator

Radians to degrees in one step.

Result

143.2394

How it is calculated

Enter the angle in radians as a plain decimal number. One half turn is π radians and also 180°, so the conversion factor is 180 ÷ π ≈ 57.2958: deg = rad × 180 ÷ π. The result is in degrees, shown to 4 decimal places. The tool does not try to wrap the angle into 0°–360°, so 7 rad gives 401.0705° rather than 41.0705°, and negative values keep their sign. Zero gives 0.0000. An empty box gives no result. Type π as a number: enter 3.14159265 rather than the symbol or the text 'pi'. Because the input is a rounded decimal, a value such as 1.5708 gives 90.0002° and not exactly 90°.

Worked example

Convert 2.5 radians. Multiply by 180: 2.5 × 180 = 450. Divide by π ≈ 3.141593: 450 ÷ 3.141593 ≈ 143.2394. The tool prints 143.2394 degrees. Sanity check: π ≈ 3.14 radians is 180°, and 2.5 is a little under 0.8 of that, so the answer should be a little under 144° (0.8 × 180).

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Common mistakes

  • Multiplying by π ÷ 180 instead of 180 ÷ π. That is the opposite conversion, and it turns 2.5 into about 0.0436, not 143.24.
  • Typing a degree value into the radians box. Entering 90 means 90 radians, which is 5,156.6202°, not a right angle.
  • Expecting the angle to be reduced to a single turn. 7 radians is shown as 401.0705°, so subtract 360° yourself if you want 41.0705°.
  • Entering π as a rounded number and expecting an exact result. 3.14 gives 179.9087°, not 180°; use more decimals, such as 3.14159265.
  • Typing text such as 'pi/2' or 1/2. The box needs a decimal number, so type 1.5707963 for π/2.

About this calculator

Radians and degrees are two different units for measuring the same thing — an angle — just as meters and feet are two units for the same length. One full circle equals 360 degrees or 2π radians, so the conversion is a straightforward ratio: degrees = radians × (180/π).

Radians are the default unit in almost every programming language’s math library (Math.sin, Math.atan2, and so on all expect radians), in calculus (derivatives of trigonometric functions only take their clean form in radians), and in physics formulas for angular velocity and angular momentum. Degrees, meanwhile, are what CAD software, protractors, navigation headings, and most everyday engineering drawings use. Converting between the two is a routine step whenever a calculation crosses from a math or physics context into a drafting, GPS, or user-facing display context.

Enter an angle in radians and this calculator applies the 180/π factor instantly to give you the equivalent in degrees.

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