555 Timer Formulas: Frequency and Duty Cycle

555 timer formulas for astable and monostable mode: frequency, high and low time, duty cycle and pulse length, with worked examples and a table.

The formulas

R is in ohms, C in farads and the times in seconds. The factor 0.693 is ln 2 and 1.1 is the rounded value of ln 3. The standard astable circuit always has a duty cycle above 50%, since tH is longer than tL. Real components and the supply voltage cause errors, so check the result on a bench.

Worked example: astable, R1 = 1 kΩ, R2 = 10 kΩ, C = 10 µF

1. tH = 0.693 × 11,000 × 0.00001 = 76.25 ms and tL = 0.693 × 10,000 × 0.00001 = 69.31 ms
2. f = 1 / (76.25 ms + 69.31 ms) = 6.87 Hz
3. D = 11 / 21 × 100 = 52.38%

Worked example: monostable, R = 10 kΩ, C = 100 µF

1. t = 1.1 × 10,000 × 0.0001 = 1.1 s

Astable output with R1 = 1 kΩ and R2 = 10 kΩ

Frequently asked questions

Why can the duty cycle not be below 50%?

The capacitor charges through R1 and R2 and discharges only through R2, so the high time is always longer than the low time. A diode across R2 or a different circuit gives a lower duty cycle.

Does the supply voltage change the frequency?

Hardly. The thresholds are set as fractions of the supply, so the timing is almost independent of it, which is one reason for the 555’s popularity.

Which capacitor should I use?

Use a stable type, such as film or ceramic C0G, for accurate timing. Electrolytic capacitors have a large tolerance and leakage.

What if I need a long delay?

Use a larger R or C, but a very large R makes the timing depend on the leakage of the capacitor and the input current of the chip.

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