Work out 555 timer astable instantly with clear inputs, formula shown and shareable results.
In astable mode the capacitor charges through R1 + R2 and discharges through R2 alone, so high time is 0.693(R1+R2)C and low time is 0.693 R2 C. Frequency is 1.44/((R1+2R2)C), and the duty cycle always exceeds 50% because charging goes through the extra resistor.
555 astable
f = 1.44 / ((R1 + 2 R2) x C); duty = (R1 + R2) / (R1 + 2 R2)
Electrical results are planning estimates only. Verify against the applicable wiring rules (IEC 60364, BS 7671, NEC or local code) and have all installation work designed and checked by a qualified electrician.
Because the charge path always includes R1 in addition to R2, so high time always exceeds low time. A diode across R2 is the usual workaround.
It is ln(2), because the capacitor swings between one third and two thirds of the supply — an exponential interval of exactly ln 2 time constants.