RC Time Constant Calculator

What the rc time constant calculator shows

An RC circuit charges and discharges its capacitor through a resistor at a rate set by the time constant. This rc time constant calculator multiplies the resistance by the capacitance to give that time constant, τ, and then the time to reach a full charge. Whether you use it as an rc circuit time constant calculator or a capacitor time constant calculator, it answers how fast the circuit responds.

The rc time constant formula

The rc time constant formula multiplies resistance by capacitance:

R is the resistance in ohms and C is the capacitance in farads, so τ comes out in seconds. In one time constant the capacitor charges to about 63 percent of the supply, and by five time constants it is over 99 percent, which counts as fully charged. This tau rc formula also governs discharge, where the voltage falls to 37 percent after one time constant.

RC circuit time constant calculator example

A 10 kΩ resistor and a 100 µF capacitor. The rc circuit time constant calculator gives:

So the time constant is 1 second, and the capacitor is fully charged after about 5 seconds. Change either component and the rc time constant calculator updates τ at once.

How to use the rc time constant calculator

Enter the resistance in ohms and the capacitance in microfarads, then the rc time constant calculator returns the time constant in seconds and milliseconds and the full charge time. Read the values from the components or the schematic. As an rc filter time constant calculator the same time constant sets the cutoff frequency of a first order filter.

Reading the rc time constant calculator result

The time constant is the time to charge to 63 percent or discharge to 37 percent. Full charge and full discharge are reached after about five time constants, so a 1 second time constant means roughly 5 seconds to settle. A bigger resistor or a bigger capacitor slows the circuit down. In a filter, a longer time constant means a lower cutoff frequency. Use the rc time calculator result to set delays, debounce times, and filter corners.

When to use the rc constant calculator

• Setting a delay or debounce with the rc constant calculator
• Sizing a filter corner with an rc filter time constant calculator
• Finding charge and discharge times of a capacitor
• Checking a design with an rc tau calculator

Common rc time constant calculator mistakes

• Wrong capacitance unit. A microfarad is a millionth of a farad; convert before you multiply.
• Thinking one tau is full charge. One time constant is 63 percent; full charge takes about five.
• Forgetting discharge uses the same tau. Charge and discharge share the time constant.

Tips for RC timing

• Use five time constants as the settle time for charge or discharge.
• Keep ohms times farads so the result is in seconds.
• For a filter, convert the time constant to a cutoff with f = 1 / (2 π τ).

Related to the rc time constant calculator

An RC circuit ties resistance and capacitance together. The capacitor energy calculator finds the energy the capacitor stores, and the Ohm’s law calculator relates the resistance to the current and voltage in the circuit. Together they describe how much charge is stored and how fast it moves.

Time constant for charging and discharging a capacitor

The graph of charging and discharging of a capacitor is an exponential curve, and the time constant is what sets its shape. When charging, the capacitor voltage rises fast at first and then levels off: 63 percent of the supply after one time constant, 86 percent after two, 95 percent after three, and over 99 percent after five, which is treated as full. Discharging mirrors this, falling to 37 percent after one time constant. The time constant for charging and discharging a capacitor is the same, τ = R × C, because the same resistor limits the current in both directions. This is why five time constants is the rule of thumb for a circuit to settle, and why the LED resistor calculator and other timing circuits lean on the same R and C values.

RC filter time constant calculator and tau

The same τ that sets the charge time also sets the behaviour of an RC filter, so an rc filter time constant calculator and an rc tau calculator are the same tool used for a different purpose. In a first order low pass or high pass filter, the cutoff frequency is f = 1 ÷ (2 π τ), so a larger time constant gives a lower cutoff. To calculate the time constant of an rc circuit you always multiply R by C, then read it as a delay for a timing circuit or convert it to a cutoff for a filter. Keep the units straight: ohms times farads gives seconds, and a microfarad is a millionth of a farad.

Time constant of rc circuit calculator values

Time constant and full charge time for common component pairs, from the time constant of rc circuit calculator:

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