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Conversions

Angle Conversion

Convert degrees, radians, gradians. Free online Angle Conversion. Calculate angle conversion online — fast, accurate, mobile-friendly, no signup needed.

All angle units
radian
0.017453
gradian
1.111111
arcminute
60
arcsecond
3,600
turn
0.002778

Derivation

  1. ├── 01Given1 degree
  2. ├── 02Formulaangle = value × (factor_from / factor_to)
  3. ├── 03Substitute1 × (0.0174532925 / 1)
  4. ├── 04Simplify1 × 0.0174532925
  5. └── 05Result0.017453 radian
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§01What is

Understanding the Angle Conversion

This tool converts values from degrees to radians. Convert degrees, radians, gradians. Whether you’re working with scientific data, engineering specs, or everyday measurements, it gives you the exact answer instantly.

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The Angle Conversion sits in that toolkit — it convert degrees, radians, gradians. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

1 degree = 0.0174533 radians → value_in_radian = value_in_degree × 0.0174533

Where

value_in_degree
The number of degrees you start with (the value you enter above)
value_in_radian
The equivalent number of radians (the result)
factor
The exact conversion ratio — 0.0174533 — anchored to SI definitions, not rounded
§03Practical Example

Step-by-step walkthrough

Scenario

Convert 5 degrees to radians.

  1. 01Look up the SI factors: 1 degree = 0.017453292519943295 base units, 1 radian = 1 base units.
  2. 02Divide to get the conversion ratio: 0.017453292519943295 / 1 = 0.0174533.
  3. 03Multiply by the quantity: 5 × 0.0174533 = 0.0872665.
  4. 04So 5 degrees = 0.0872665 radians.
§04Variants

Common Angle Conversion Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

1 degree

radians = degrees × 0.0174533

Convert 1 degree to radians.

  1. 01Start with 1 degree.
  2. 02Multiply by the conversion ratio 0.0174533.
  3. 03Result: 1 degree = 0.0174533 radians.
02 · PATTERN

10 degrees

radians = degrees × 0.0174533

Convert 10 degrees to radians.

  1. 01Start with 10 degrees.
  2. 02Multiply by the conversion ratio 0.0174533.
  3. 03Result: 10 degrees = 0.174533 radians.
03 · PATTERN

100 degrees

radians = degrees × 0.0174533

Convert 100 degrees to radians.

  1. 01Start with 100 degrees.
  2. 02Multiply by the conversion ratio 0.0174533.
  3. 03Result: 100 degrees = 1.74533 radians.
§05FAQ

Frequently asked questions

No — 1 degree is smaller, it equals only 0.0174533 radians.
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