Formula
Astable high time is ln(2) × (R1 + R2) × C. Low time is ln(2) × R2 × C. Frequency is the reciprocal of the sum. Duty cycle is the high time over the period, which simplifies to (R1 + R2) / (R1 + 2 R2) and is always above 50% for a positive R1. Data sheets often print 1.44 in front of the frequency. 1/ln(2) is 1.442695, so 1.44 is that constant rounded. This page keeps ln(2).
tHigh = ln(2) (R1 + R2) C
tLow = ln(2) R2 C
tPulse = 1.1 R C
The monostable pulse uses 1.1, the constant on the TI LM555 data sheet, not ln(3). Nearest parts are E24 resistors and an E12 capacitor, the two series most timing kits are stocked in. A CMOS timer can charge through a different network. The RC time constant page is the exponential those intervals come from.
Worked examples
R1 = 1 kΩ, R2 = 10 kΩ, C = 10 nF, astable. High 76.25 µs, low 69.31 µs, frequency 6,870 Hz, duty 52.38%.
R = 100 kΩ, C = 10 µF, monostable. Pulse 1.100 s.
Those parts are already standard. The nearest line repeats 1 kΩ, 10 kΩ, and 10 nF, or 100 kΩ and 10 µF.
Reference
ln(2) is 0.693147. 1/ln(2) is 1.4427. The monostable factor on this page is 1.1 exactly.
Questions
What frequency is 1 kΩ, 10 kΩ, and 10 nF?
6,870 Hz. High time is ln(2) × 11 kΩ × 10 nF. Low time is ln(2) × 10 kΩ × 10 nF. Duty cycle is 52.38%, which is (R1 + R2) / (R1 + 2 R2).
Why not 1.44?
1.44 is 1/ln(2) rounded. This page uses ln(2) itself, so the period is exact for the ideal bipolar timing identity. A CMOS 555 data sheet can print a slightly different charge equation. Read the part you buy.
What is the monostable constant?
1.1, the figure printed on the TI LM555 data sheet. ln(3) is 1.0986. The page uses 1.1 so a 100 kΩ and 10 µF pulse is 1.100 s.
Sources
- Bipolar 555 astable timing with ln(2). The familiar 1.44 is 1/ln(2) rounded.
- TI LM555 data sheet, monostable time 1.1 RC.
- IEC 60063 E24 resistors and E12 capacitors for the nearest-part line.