RC Circuit Calculator: Time Constant, Capacitor Charge and Discharge, Cut-off Frequency and Energy

Find how a capacitor charges and discharges through a resistor and the cut-off frequency of an RC filter.

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

Enter the resistance, the capacitance, the supply voltage, a time and a percentage of the final voltage.

The calculator finds the time constant R x C, the capacitor voltage after charging and after discharging for the time you gave, the current at that time, and the time to reach the percentage.

It also gives the cut-off frequency 1 over 2 pi R C of the RC filter and the energy one half C V squared.

Formulas used

  • \tau = RC
  • v_C = V_s(1 - e^{-t/\tau})
  • v_C = V_s e^{-t/\tau}
  • f_c = \frac{1}{2\pi RC}
  • E = \tfrac12CV^2

Worked example

With the default numbers in the calculator above:

  1. Time constant: 1.00 s
  2. Capacitor voltage after charging for the time you gave: 3.16 V (63.21 percent of the supply)
  3. Capacitor voltage after discharging for the same time (starting from the supply voltage): 1.84 V
  4. Current at that time (charging or discharging): 0.18 mA (starting at 0.50 mA)
  5. Time to charge to the percentage you gave: 1.00 s (1.00 time constants)
  6. Time to be considered fully charged (5 time constants, 99.3 percent): 5.00 s
  7. Cut-off frequency of the RC filter (the output is down 3 dB): 0.16 Hz
  8. Energy stored when fully charged: 0.00125 J (1.25 mJ)

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

Common questions

What is a time constant?

The time for a charging capacitor to reach 63.2 percent of its final voltage, or for a discharging one to fall to 36.8 percent.

How long does it take to charge fully?

About five time constants, when it is at 99.3 percent.

What is the cut-off frequency?

The frequency at which the output of an RC filter is down by 3 dB, which is 70.7 percent of the input.

Is the energy lost in the resistor?

When charging from a fixed voltage, half the energy from the supply is stored and half is lost as heat in the resistor, whatever the resistance.

Related calculators

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

Further reading: Horowitz and Hill, The Art of Electronics; any circuit analysis text (first-order circuits).

Need a calculator we do not have?

Tell us what you would like to calculate. We read every request and build the most asked-for ones.

We store your request (and your email if you give it) to decide what to build. We do not store the numbers you type into calculators.

Embed this calculator on your own page

Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.

Need this drawn, designed or checked?

Drafting Central is a mechanical engineering and drafting business working with customers across Australia and around the world. A calculator gives you the numbers; we can turn them into drawings and designs.

Need help with a real project?

Talk to Drafting Central →

← All engineering calculators