Formula & Calculator
Hobby Servo Pulse-Width to Angle Mapping
Converts a standard hobby servo's PWM control pulse width into the corresponding commanded shaft angle, based on the common 1000-2000 microsecond range.
Interpretation
θ = (pulse_width − 1000)/(2000−1000)×180. Maps pulse width (µs) to angle (°) for typical servos. Used in servo control.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| theta | Commanded servo angle | degrees |
| pulse_width | PWM control pulse width | microseconds |
What it means
Standard hobby servos use a 50 Hz PWM signal, with pulse widths from 1000 µs to 2000 µs corresponding to 0° to 180°. This linear mapping is used to generate the appropriate pulse width for a desired angle. Understanding this is essential for controlling servos with microcontrollers.
Worked example
Servo Pulse‑Width to Angle – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| pulse_width (μs) | 1500 |
| Parameter | Value |
|---|---|
| pulse_width | 1250 |
Common mistakes
- Servo pulse‑width to angle mapping: θ = (pulse_width − 1000) / (2000 − 1000) × 180 – for common 1000‑2000 µs range.
- Assumes: Linear mapping, 180° range (some servos have smaller ranges).
- Units: pulse_width in microseconds – typical range 1000‑2000 µs.
- Center position: 1500 µs corresponds to 90°.
- Limits: Some servos have different ranges – check the datasheet.
Applications
Hobby servo pulse‑width to angle mapping, θ = (pulse_width − 1000)/(2000 − 1000)×180, converts a pulse width (in microseconds) to the corresponding angular position for standard RC servos. This is used to command servos in robotics, animatronics, and model aircraft. Engineers and hobbyists use it to map desired angles to PWM signals, allowing precise positioning of joints and control surfaces. By understanding this mapping, they can interface microcontrollers with servos and implement closed‑loop control. This formula is a fundamental tool for servo‑based actuation.
- Position control of servo motors in robotics and animatronics
- Control surface deflection in RC aircraft and drones
- Gripper and end‑effector actuation in pick‑and‑place systems
- Calibration and programming of servos for precise positioning
- Integration with microcontrollers (Arduino, Raspberry Pi, etc.)
Frequently Asked Questions
The servo angle is linearly mapped from the pulse width (in microseconds). A common mapping is θ = (pulse_width – 1000) / (2000 – 1000) × 180 for a 0‑180° range, assuming pulse widths from 1000 to 2000 µs.
Assuming a universal 1000‑2000 µs pulse range for all servos. Many servos actually use a different range (e.g., 500‑2500 µs) specified in their datasheet. Always check the servo's specifications.
Typically, 1 ms corresponds to 0° and 2 ms to 180° for many servos. Some servos use 0.5 ms to 2.5 ms for 0‑180°.
pulse_width = (angle / 180) × (max_pulse – min_pulse) + min_pulse.
Most servos have a resolution of about 1 µs, which corresponds to about 0.09° for a 1000‑2000 µs range and 180° span.
Using a PWM signal with a period of 20 ms (50 Hz), and a variable pulse width. The pulse width determines the angle.
Jitter in the pulse width causes the servo to oscillate or not hold position accurately. Using a stable PWM signal is important.
Limited torque, speed, and precision compared to industrial servos. They are suitable for low‑cost, light‑duty applications.
Send the minimum and maximum pulse widths and measure the resulting angles; then use those values in the mapping formula.
Robotics (small arms, grippers), RC vehicles, and mechatronics projects.