Degrees to Radians
Convert degree to radian instantly — type a value and read the result, with the exact formula shown.
Example
1 ° = 0.01745329 rad, 5 ° = 0.08726646 rad, 10 ° = 0.1745329 rad.
How it works
Radian = Degree × 0.01745329. Every value is converted through a single degree base unit using internationally defined conversion factors, so any from/to pair stays consistent.
Good to know
Converting degrees to radians is the bridge between how humans usually describe angles and how the math behind them actually works. You reach for radians whenever you feed an angle into trigonometry on a computer, a calculator, or a programming language: functions like Math.sin(), cos(), and tan() in JavaScript, Python, C, and nearly every other language expect their input in radians, not degrees. Engineers, game developers, robotics programmers, and physics students all hit this conversion constantly when computing rotations, oscillations, and circular motion.
The two units come from very different traditions. The degree is an ancient unit, splitting a full turn into 360 parts — a choice usually traced to Babylonian astronomers and their base-60 number system, which divides cleanly by many factors. The radian is the modern, "natural" unit of angle: one radian is the angle you get when the arc length along a circle equals its radius. That definition ties angles directly to a circle's geometry, which is exactly why calculus and physics formulas come out clean in radians and messy in degrees.
The whole conversion hangs on one fact: a full circle is 360° and also 2π radians, so 180° = π radians. To go from degrees to radians, multiply by π/180 (about 0.01745329). A handy rule of thumb: a single degree is roughly 0.0175 rad, and conveniently 1 radian is just under 57.3° — close to "60 degrees minus a bit." For quick mental checks, memorize the landmark angles:
- 30° = π/6 ≈ 0.5236 rad, 45° = π/4 ≈ 0.7854 rad, 60° = π/3 ≈ 1.0472 rad, 90° = π/2 ≈ 1.5708 rad, and 180° = π ≈ 3.1416 rad.
The most common mistake is forgetting to convert at all — passing 90 into a sine function and expecting 1, when the function reads 90 as 90 radians and returns roughly 0.894. The other trap is precision: radians are usually irrational multiples of π, so any decimal result is rounded. If exactness matters, keep the answer as a fraction of π (like π/4) rather than 0.7853981, and only round at the very end of a calculation.
Frequently asked questions
How do you convert degree to radian?
Multiply the number of degrees by 0.01745329 to get radians. For example, 1 ° = 0.01745329 rad.
What is 1 degree in radians?
1 degree equals 0.01745329 radians (1 ° = 0.01745329 rad).
How many degrees are in 1 radian?
There are 57.29578 degrees in 1 radian.
Is this converter free and private?
Yes. It runs entirely in your browser, so your inputs never leave your device, there is no sign-up, and it works offline once loaded.
Are the conversions exact?
Conversions use internationally defined factors and are exact where the definitions are exact (for example, 1 inch = 2.54 cm). Displayed results are rounded for readability.
People also ask
What is the formula to convert degrees to radians?
Multiply the degree value by π/180, which is approximately 0.01745329. So radians = degrees × π ÷ 180.
How many radians is 90 degrees?
90 degrees equals π/2 radians, which is about 1.5708 rad.
How many radians is 180 degrees?
180 degrees equals exactly π radians, approximately 3.14159 rad. This is the defining relationship used for the conversion.
What is 45 degrees in radians?
45 degrees equals π/4 radians, or about 0.7854 rad.
What is 360 degrees in radians?
360 degrees is one full turn, which equals 2π radians, approximately 6.28319 rad.
Why do calculators and programming languages use radians instead of degrees?
Trigonometric functions in math, calculus, and most programming languages (like sin, cos, and tan) are defined using radians because it makes their formulas and derivatives clean. Passing degrees directly gives wrong answers unless you convert first.
What is 30 degrees in radians?
30 degrees equals π/6 radians, which is about 0.5236 rad.
How do I convert 60 degrees to radians?
Multiply 60 by π/180 to get π/3 radians, approximately 1.0472 rad.
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