RC Time Constant Calculator: tau = R x C

How fast a capacitor charges or discharges through a resistor.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • \tau = RC
  • R = \frac{\tau}{C}
  • C = \frac{\tau}{R}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the time constant: time constant = resistance x capacitance
  2. Put the values in (every value in its SI unit): time constant = 10000 x 0.0001
  3. The answer: time constant: 1 s
  4. The same answer in other units: 1000 ms; 1.0e+6 us; 5 seconds to charge to 99 percent (5 time constants)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Capacitance; Time constant (leave it as it is if this is what you are finding) 1 s; Resistance (leave it as it is if this is what you are finding) 10000 ohm.

  1. The formula, arranged to find the capacitance: capacitance = (time constant) / (resistance)
  2. Put the values in (every value in its SI unit): capacitance = (1) / (10000)
  3. The answer: capacitance: 0.0001 F
  4. The same answer in other units: 100 uF; 100000 nF; 0.1 mF

Common questions

What is the RC time constant?

The product of the resistance and the capacitance. It is the time for the voltage to reach 63.2 percent of its final value.

How long does a capacitor take to charge fully?

About 5 time constants, when it reaches 99 percent.

How do I make a slower circuit?

Increase either the resistance or the capacitance.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any electrical text (RC circuits).

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