How many radians are in a turn?

One full turn (complete revolution) is exactly 2π radians, which is about 6.28318 rad.

What is the formula to convert turns to radians?

To convert turns to radians, multiply by 2π. The formula is rad = turns × 2π.

Where is turns to radians conversion used?

Turns to radians is used in trigonometry, rotational motion, signal processing, robotics and any situation where full rotations are converted to the radian measure used in maths and physics.

Turns to radians – convert turns to rad

Convert turns to radians (turn to rad) for circles, rotations and trigonometry problems. This page opens the main angle converter with turn → rad pre-selected.

Open the interactive turns → radians converter:

Use main converter (turn → rad) or switch to rad → turn

On the homepage you can also convert between degrees, radians, gradians and turns.

Quick reference: turns to radians

One full turn is 2π radians (≈ 6.28318 rad), so: radians = turns × 2π. Examples:

Angle (turns)	Angle (radians, approx.)
0.25 turns	1.571 rad
0.5 turns	3.142 rad
1 turn	6.283 rad
1.5 turns	9.425 rad
2 turns	12.566 rad

Why convert turns to radians?

Turns to radians is useful when you:

Translate intuitive “number of rotations” into radian measure.
Work with trigonometric functions that use radians by default.
Model rotating machinery, wheels or motors in physics or engineering.
Analyse periodic signals and waveforms in maths or signal processing.

Other angle converters on this site

Radians are the natural angle unit in most maths and physics formulas, which is why many calculators default to rad mode.

Page last updated: 4 December 2025.