# What is 0.693, and 1.1, and 1.44 in IC 555 Calculations

I tried a lot to figure out but could not find any answer to this question anywhere.

For calculating pulse width in a standard IC 555 astable and monostable configurations we use the following formulas respectively:

T(high) ≈ 0.693(R1 + R2)C1

T = 1.1RC

And for the frequency we use the formula:

F = 1.44/((R1+2R2)C1

I am interested to know how the constants 0.693, 1.1, and 1.44 were derived in the respective calculations?

• have schema , easier to compute, or read datasheet or App Note!! – Tony Stewart Sunnyskyguy EE75 Aug 24 '19 at 7:14
• First, see what you can work out yourself. Look at the internal circuit for the 555, you'll see two comparators with trip points of 1/3rd supply voltage and 2/3rds supply voltage. Then take the equations for RC charging and RC discharging and try to produce equations that fit the 555 circuit for charging and discharging. Note that 1.44 is the approx. reciprocal of 0.693. Work at it rather than wait for answers, you'll learn more this way. – TonyM Aug 24 '19 at 7:22
• electronics-tutorials.ws/waveforms/555_timer.html you may start here – User323693 Aug 24 '19 at 7:46
• @Tony, Thanks, Yes I can surely investigate it, however I would rather appreciate a quick solution because I have some other related problems which I want to solve after knowing this answer. – Swagatam Majumdar Aug 24 '19 at 10:53
• Yes, you surely can investigate it, as a passionate researcher and developer. After all, you said this was interest :-) The purpose of the site is to educate and not to be an online technical encyclopedia, copied out to you on demand. There is plenty about this old, old chip on the interweb. Handing over answers is not what this site's about. – TonyM Aug 24 '19 at 11:21

The precise numbers are:

• ln(2) = 0.693147
• ln(3) = 1.098612
• 1 / ln(2) = 1.442695

It's a good exercise for you to figure out how these numbers arise from the analysis of the circuit operation.

The key facts about the 555 are:

• In monostable operation, the timing capacitor charges through a resistance from 0V to 2/3 Vcc.

• In astable operation, the timing capacitor voltage cycles between 1/3 Vcc and 2/3 Vcc.

• Great! Thanks very much for the clues, I'll check them out! – Swagatam Majumdar Aug 25 '19 at 12:20