Servo Duty Cycle Calculation Formula: The Complete Guide for Precise Angular Control

01Core Formula

The duty cycle for aservois derived from the required pulse width and the fixed PWM period:

Duty Cycle (%) = (Pulse Width (ms) / PWM Period (ms)) × 100%

For standard analog and digital servos, the PWM period is20 milliseconds (ms), corresponding to a frequency of 50 Hz.

02Step-by-Step Calculation for Any Desired Angle

If you need an angle θ between 0° and 180°,the pulse width is calculated using linear interpolation:

Pulse Width (ms) = 0.5 + (θ / 180) × 2.0

Then apply the duty cycle formula.

03Direct Duty Cycle Formula (0° to 180°)

Combine both steps into one formula:

Duty Cycle (%) = [0.5 + (θ × 2.0 / 180)] / 20 × 100

Simplified:

Duty Cycle (%) = 2.5 + (θ × 10 / 180)orDuty Cycle (%) = 2.5 + (θ / 18)

Verification:

At 0°: 2.5% → (0.5 ms /20 ms)=2.5% ✓

At 90°: 2.5 + 5 = 7.5% ✓

At 180°: 2.5 + 10 = 12.5% → (2.5 ms/20 ms)=12.5% ✓

04Important Notes on Servo Types

Standard servos(0°–180°): Use the formulas above.

Continuous rotation servos: Duty cycle controls speed and direction, not angle. A 7.5% duty cycle typically means stop; values below or above cause rotation in opposite directions.

Extended range servos(e.g., 0°–270°): Adjust the pulse width range accordingly (commonly 0.5 ms to 3.0 ms for 270°). Recalculate the linear mapping.

Digital servos: Accept the same PWM signals but can operate at higher frequencies (e.g., 200–333 Hz). Always check the servo datasheet; if not specified, default to 50 Hz.

05Common Mistakes to Avoid

1. Using the wrong period: A 20 ms period (50 Hz) is standard. Using 10 ms (100 Hz) will cut all duty cycle values in half, resulting in incorrect angles.

2. Miscalculating pulse width limits: Never send pulse widths below 0.5 ms or above 2.5 ms for standard servos. This can cause jitter, overheating, or mechanical damage.

3. Inverting the formula: Duty cycle is (pulse width / period), not (period / pulse width). The latter would give a value >100% and is invalid.

4. Forgetting to convert units: Ensure both pulse width and period are in the same unit (both ms or both µs). 20 ms = 20,000 µs.

06Practical Action Steps

1. Verify your servo’s specifications– Locate the datasheet or measure the minimum and maximum pulse widths using an oscilloscope or a servo tester. Do not assume 0.5–2.5 ms without confirmation.

2. Calculate your target duty cycleusing the direct formula: Duty (%) = 2.5 + (desired angle / 18).

3. Implement in code– For example, using Arduino’sanalogWrite()orservo.write(), but for low-level PWM control, compute the compare register value:OCR = (duty_cycle / 100) × timer_top.

4. Test at neutral (90°)first. If the servo does not center at 7.5% duty cycle, adjust the offset in your formula.

5. Gradually test extreme angles– Command 0° and 180° while listening for stalling or buzzing, which indicates pulse width limits are exceeded.

07Final Summary

The relationship between servo angle and duty cycle is linear and governed by a single equation:Duty Cycle (%) = (Pulse Width in ms / 20) × 100, where Pulse Width = 0.5 + (θ × 2/180). For quick field calculations, useDuty (%) = 2.5 + (θ / 18). Always confirm your servo’s specific pulse range before deployment. Apply this formula to achieve precise, repeatable angular positioning in robotics, automation, and control systems.