315 Degrees to Radians

315° = 7π/4 rad

315 degrees equals 7π/4 rad, which is about 5.497787 radians.

Step by step

Multiply by π/180: 315 × π/180.
Simplify the fraction: 7π/4 rad.
As a decimal (π ≈ 3.14159): 5.497787 rad.

Details

Radians (π form): 7π/4 rad
Radians (decimal): 5.497787
Gradians: 350
Turns: 0.875
sin / cos / tan: -0.707107 / 0.707107 / -1
Position: Quadrant 4

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
240°	4π/3 rad (4.1888)
255°	17π/12 rad (4.4506)
270°	3π/2 rad (4.7124)
285°	19π/12 rad (4.9742)
300°	5π/3 rad (5.236)
315°	7π/4 rad (5.4978)
330°	11π/6 rad (5.7596)
345°	23π/12 rad (6.0214)
360°	2π rad (6.2832)

Related conversions

Frequently asked questions

What is 315 degrees in radians?

7π/4 rad ≈ 5.497787 rad.

How do you convert 315° to radians?

Multiply 315 by π/180.

What are sin, cos and tan of 315°?

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

How many degrees is 5.4978 radians?

About 315°.