Calculate square wave frequency, period, duty cycle, and high/low times from timing values or 555 astable resistor and capacitor inputs.
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Square Wave Frequency Formula
Choose the conversion or timing mode that matches the values you know.
Period and frequency:
Pulse times and duty cycle:
555 timer astable mode:
- f = frequency in hertz (Hz)
- T = period in seconds (s)
- t_high = time the signal is high
- t_low = time the signal is low
- D = duty cycle as a percentage
- R1, R2 = timing resistors in ohms (Ω)
- C = timing capacitor in farads (F)
The 555 formula assumes a standard astable circuit where C charges through R1 + R2 and discharges through R2 only. This always produces a duty cycle above 50%. Modified diode circuits or other topologies need their own timing equations; adding a diode alone does not guarantee exactly 50% duty. Actual timing also depends on component tolerances and the timer’s operating limits.
Reference Tables
Common period and frequency pairs you can use to sanity-check a result:
| Frequency | Period | Half cycle |
|---|---|---|
| 1 Hz | 1 s | 500 ms |
| 60 Hz | 16.67 ms | 8.33 ms |
| 1 kHz | 1 ms | 500 µs |
| 38 kHz | 26.32 µs | 13.16 µs |
| 1 MHz | 1 µs | 500 ns |
| 16 MHz | 62.5 ns | 31.25 ns |
Illustrative waveform frequencies by application (check the actual device specifications):
| Application | Typical range |
|---|---|
| LED blink / heartbeat | 1 Hz to 10 Hz |
| Audio tones | 20 Hz to 20 kHz |
| Servo PWM | 50 Hz |
| Motor / LED PWM | 500 Hz to 25 kHz |
| IR remote carrier | 36 kHz to 40 kHz |
| Switching power supplies | 50 kHz to 1 MHz |
| Microcontroller clocks | 1 MHz to 200 MHz |
Worked Example
Problem: A 555 astable uses R1 = 4.7 kΩ, R2 = 10 kΩ, and C = 0.1 µF. Find the frequency and duty cycle.
Solution:
- R1 + 2·R2 = 4,700 + 20,000 = 24,700 Ω
- (R1 + 2·R2) · C = 24,700 × 0.0000001 = 0.00247 s
- f = 1.4427 / 0.00247 ≈ 584 Hz
- t_high = 0.693 × (R1 + R2) × C ≈ 1.018 ms
- t_low = 0.693 × R2 × C ≈ 0.693 ms
- Duty cycle = 1.018 / (1.018 + 0.693) ≈ 59.5%
FAQ
Is a square wave always 50% duty? A pure square wave is 50%. Anything else is a rectangular or pulse wave, but the period-to-frequency math is the same.
Why does my 555 never reach 50%? The standard astable charges through R1 + R2 and discharges through R2 alone, so t_high is always longer than t_low. Make R1 small relative to R2 to get close to 50%, or add a steering diode.
What is angular frequency? ω = 2πf, in radians per second. It is mostly used in phase and Fourier calculations, not in pulse timing.
