My gyroscope reports 9,424.8 mrad of total rotation. How many turns did the object complete?

9,424.8 ÷ 6,283.185 = 1.5 turns (= 540°). The object completed one full rotation plus a half rotation.

A stepper motor specification says 200 steps per turn. My sensor reads 62.83 mrad. How many steps is that?

62.83 ÷ 6,283.185 = 0.01 turns × 200 steps/turn = 2 steps. Converting mrad to turns first, then multiplying by steps/turn gives the step count directly.

Why would a ballistics system ever need to output in turns?

Unusual for field targeting, but common in robotics integration: a weapon stabilizer outputting mrad/s angular rate data feeds into a robotic chassis controller that expects rad/s or turns/s for motor velocity commands.

How many milliradians are in a quarter turn exactly?

0.25 × 2,000π = 500π ≈ 1,570.796 mrad. This is π/2 radians expressed in milliradians — the value for a 90° right-angle rotation.

Milliradians to Turns Converter

Enter a value to instantly convert between angle units.

From

Precision4 dp

1 Milliradian = 0.0002 Turn

Key Formulas

Degree → Radian

rad = ° × 0.0174533

Radian → Degree

° = rad × 57.2958

Degree → Gradian

grad = ° × 1.11111

Gradian → Degree

° = grad × 0.9

Formula

turns = mrad ÷ 6283.185

Inertial sensors and gyroscopes in navigation and stabilization systems output angular measurements in milliradians or mrad/s, while servo motors and robotic joints are commanded in fractional turns or revolutions. A drone's stabilization system reading 3,141.6 mrad of roll rotation must translate that to 0.5 turns for the gimbal motor controller. The divisor 6,283.185 is 2π × 1,000 — the number of milliradians in one complete revolution.

Source: ISO 80000-3:2019 (Quantities and units — Space and time)

Last reviewed: 2026-06-11 · see our methodology

Frequently Asked Questions

Real-World Examples

6,283.185 mrad — exactly 1 full turn (2π radians, 360°). The conversion constant equal to 2,000π milliradians per revolution.

6283.185 mrad = 1 tr

3,141.6 mrad — exactly half a turn (π radians, 180°). The IMU reading after a drone completes a 180° yaw maneuver, converted to turns for the flight log.

3141.593 mrad = 0.5 tr

1,570.8 mrad — a quarter turn (π/2 radians, 90°). A robotic arm joint's 90° rotation expressed in turns for the motion planner.

1570.796 mrad = 0.25 tr

628.3 mrad — one-tenth of a turn (36°). A gimbal's small rotation expressed as a fractional turn for an animation system interpolating camera movement.

628.318 mrad = 0.1 tr

degrees to radians radians to degrees degrees to gradians gradians to degrees

Milliradians to Turns Converter

Key Formulas

Formula

Frequently Asked Questions

Real-World Examples

Related Converters