45 Degrees to Radians

45° = π/4 rad

45 degrees equals π/4 rad, which is about 0.785398 radians.

Step by step

Multiply by π/180: 45 × π/180.
Simplify the fraction: π/4 rad.
As a decimal (π ≈ 3.14159): 0.785398 rad.

Details

Radians (π form): π/4 rad
Radians (decimal): 0.785398
Gradians: 50
Turns: 0.125
sin / cos / tan: 0.707107 / 0.707107 / 1
Position: Quadrant 1

How it works

A full turn is 360 degrees or 2π radians, so 180° equals π radians. To convert degrees to radians, multiply by π/180 and simplify the fraction; to convert back, multiply by 180/π. Radians are the standard angle unit in mathematics, physics and programming languages, where trigonometric functions expect their input in radians.

Nearby values

Degrees	Radians
0°	0 rad (0)
15°	π/12 rad (0.2618)
30°	π/6 rad (0.5236)
45°	π/4 rad (0.7854)
60°	π/3 rad (1.0472)
75°	5π/12 rad (1.309)
90°	π/2 rad (1.5708)
105°	7π/12 rad (1.8326)
120°	2π/3 rad (2.0944)

Related conversions

Frequently asked questions

What is 45 degrees in radians?

π/4 rad ≈ 0.785398 rad.

How do you convert 45° to radians?

Multiply 45 by π/180.

What are sin, cos and tan of 45°?

0.707107 / 0.707107 / 1 (sin / cos / tan).

How many degrees is 0.7854 radians?

About 45°.