Engineering calculators

RC Time Constant Calculator

Updated Aug 30, 2026 By Jehan Wadia
Rate Formulas

Core Variable Solver — R, C, τ

Enter any two of Resistance, Capacitance and Time Constant — the third is solved automatically. SI shorthand is accepted (22k, 47u, 100n, 3.3M) and overrides the unit menu.
Solve for
Series resistance. Must be greater than zero.
Capacitor value. Must be greater than zero.
τ = R × C. Must be greater than zero.

Voltage & Transient Mode

Scales the chart, current and energy outputs.
Capacitor voltage at t = 0.
Transient Mode
Discharge auto-sets Vinitial to Vin.

Primary Outputs

Time Constant (τ)—τ = R × C
Settling Time (5τ)—99.3% of final value
RC Cutoff Frequency (fc)—−3 dB point
Rise Time 10% → 90%—2.197 × τ
Rise Time 20% → 80%—ln(4) × τ
Half-Voltage Time (t½)—τ × ln 2
Peak Transient Current (Ipeak)—at t = 0
Final Voltage (Vfinal)—steady state
Energy Stored in Capacitor (WC)—½ C V_final²
Resistor Pulse Energy (WR)—per transient event
Reactance at fc (XC)—= R at f_c
Charge Transferred (ΔQ)—C × |V_final − V_initial|

Status

Track A — Circuit Status
Track B — Electrical Response Speed

Transient Waveform (0 → 5τ)

Time cursor: —
Click the chart area then use ← / → arrow keys to move the time cursor. Dashed vertical guides mark 1τ through 5τ.

τ Milestone Table

Capacitor voltage, charge percentage and current at each time constant.
Time Actual Time VC Charge % Current

Advanced Options

Analysis Time Snapshot
Leave blank to skip the snapshot.
Design Verification
Bleed Resistor
Capacitor Properties
Enables over-voltage & margin checks.
Component Stress
Application & Frequency Analysis

Detail Outputs

Step-by-Step Solution

Introduction

The RC Time Constant Calculator helps you find how fast a capacitor charges or discharges through a resistor. Enter any two values — resistance (R), capacitance (C), or time constant (τ) — and the tool solves for the third one.

The time constant, written as the Greek letter tau (τ), equals R × C. After one time constant, a capacitor charges to about 63.2% of the supply voltage. After five time constants (5τ), it is 99.3% charged, which most engineers call "fully charged."

This calculator gives you more than just τ. It also shows:

  • Settling time (5τ) and half-voltage time
  • Cutoff frequency (fc) for RC filters
  • Rise times from 10% to 90% and 20% to 80%
  • Peak inrush current and stored energy
  • A live chart of voltage, current, and power over time

You can type shorthand like 22k, 47u, or 100n and the tool reads it right away. Advanced options let you check part tolerances, capacitor voltage ratings, bleed resistors, and nearest E12 or E24 standard values from a standard resistor series.

Use it to design timers, filters, delay circuits, snubbers, and power supply networks — and see the step-by-step math behind every answer.

How to use our RC Time Constant Calculator

Enter any two of resistance, capacitance, and time constant, then add your supply voltage. The calculator solves the missing value and shows the time constant, settling time, cutoff frequency, rise times, peak current, stored energy, a charge and discharge chart, and a step-by-step solution.

Solve for: Pick which value you want the calculator to find — Resistance (R), Capacitance (C), or Time Constant (τ). Fill in the other two boxes.

Resistance (R): Type the series resistor value and pick mΩ, Ω, kΩ, or MΩ. You can also type shorthand like 22k or 3.3M. If you only have color bands to work from, decode them with the Resistor Color Code Calculator first.

Capacitance (C): Type the capacitor value and pick pF, nF, µF, mF, or F. Shorthand like 47u or 100n works too. For series and parallel capacitor networks, the Capacitor Calculator gives you the combined value to enter here.

Time Constant (τ): Type the RC time constant and pick ns, µs, ms, or s. Leave it blank if you want the calculator to solve for it.

Supply Voltage (Vin): Enter the voltage feeding the RC circuit. This sets the current, energy, and chart values.

Initial Voltage (Vinitial): Enter the capacitor voltage at the start (t = 0). Use 0 for a fully empty capacitor.

Transient Mode: Choose Charge, Discharge, or Both. Discharge sets the starting voltage equal to Vin for you.

Analysis Time (t): Optional. Enter a time to see the exact voltage, current, and power at that moment. Leave blank to skip it.

Target Time Constant (τtarget): Optional. Enter the τ you want, and the tool shows how far off your circuit is and what R or C you need.

Capacitance Tolerance (%): Optional. Enter the capacitor's tolerance to see the worst-case high and low time constant. The Percent Error Calculator is handy if you want to compare a measured τ against the nominal one.

Resistance Tolerance (%): Optional. Enter the resistor's tolerance so the worst-case τ range includes both parts.

Bleed Resistor (Rbleed): Optional. Enter a bleed resistor value to see how fast the capacitor drains to a safe level.

DC Working Voltage Rating: Optional. Enter the capacitor's rated voltage to get over-voltage and safety margin warnings.

Capacitor Type: Optional. Pick ceramic, electrolytic, tantalum, film, or supercapacitor to get notes about real-world behavior.

Switch / Diode Current Rating: Optional. Enter the part's current limit to check if the inrush current is too high. Use the Amp Calculator to convert between current, voltage, and power ratings if your datasheet lists watts instead.

Charge–Discharge Cycle Frequency: Optional. Enter how often the circuit cycles to get the average resistor power.

Application Context: Optional. Pick your use case, like timer, filter, or snubber, for tips that match your design.

Frequency of Interest (f): Optional. Enter a frequency to see reactance, impedance, phase angle, and filter attenuation at that point. For a deeper AC breakdown, try the Impedance Calculator.

What Is the RC Time Constant?

When you connect a resistor (R) and a capacitor (C) together, the capacitor does not charge up right away. It fills with charge slowly, like water filling a bucket through a thin pipe. The RC time constant, written with the Greek letter tau (τ), tells you how fast that happens.

The formula is simple:

τ = R × C

Put resistance in ohms (Ω) and capacitance in farads (F), and you get the time constant in seconds. Bigger resistance or bigger capacitance means a slower circuit.

What Happens at Each Time Constant

After one time constant, a charging capacitor reaches about 63.2% of the supply voltage. It never quite hits 100%, but it gets very close. Engineers use these steps:

  • 1τ — 63.2% charged
  • 2τ — 86.5% charged
  • 3τ — 95.0% charged
  • 4τ — 98.2% charged
  • 5τ — 99.3% charged (treated as "done")

Discharging works the same way, just backwards. After 1τ the capacitor still holds 36.8% of its starting voltage, and after 5τ it is nearly empty. The exponential shape here is the same one behind radioactive half-life and exponential growth problems.

Key Formulas

  • Charging: vC(t) = Vfinal + (Vinitial − Vfinal) × e−t/τ
  • Cutoff frequency: fc = 1 / (2πRC)
  • Peak current: Ipeak = ΔV / R (happens right at t = 0, straight from Ohm's law)
  • Rise time (10%–90%): 2.197 × τ
  • Stored energy: W = ½ × C × V²

Why It Matters

The time constant shows up all over electronics. It sets the delay in timer circuits like the 555. It sets the corner frequency of low-pass and high-pass filters, which decide what signals get through and what gets blocked — see the Low Pass Filter Calculator for that side of the design. It controls how fast a power supply bulk capacitor recovers after a load spike, and how long a bleed resistor takes to drain a charged capacitor to a safe voltage.

The same math also warns you about danger. A big capacitor charging through a small resistor pulls a large spike of current at the very first instant. That spike can blow a switch, a diode, or a fuse even though the average current is tiny. When that resistor sits in a divider or an LED string, check the companion Voltage Divider Calculator and LED Resistor Calculator too.

Things That Change Real Results

Real parts are not perfect. Resistors and capacitors have tolerance, often ±5%, ±10% or ±20%, so your real τ will drift from the number on paper. Class II ceramic caps (X5R, X7R, Y5V) lose a lot of their value under DC voltage, which makes the circuit faster than expected. Electrolytic caps have extra internal resistance (ESR) that adds to R — and if several resistors sit in parallel, the Parallel Resistor Calculator gives the true value to plug in. Long supply runs add their own resistance as well, which the Wire Resistance Calculator and Voltage Drop Calculator can quantify. For anything that must hit a tight timing target, use tight-tolerance film or C0G/NP0 parts.

Quick Reference

  • 1 kΩ × 1 µF = 1 ms
  • 1 MΩ × 1 µF = 1 s
  • 10 kΩ × 100 nF = 1 ms
  • 1 kΩ × 1 nF = 1 µs

Formulas used

Time constant (and rearrangements for R and C)
\tau = R \times C \qquad R = \frac{\tau}{C} \qquad C = \frac{\tau}{R}
Capacitor voltage during transient
v_C(t) = V_{final} + (V_{initial} - V_{final})\, e^{-t/\tau}
Circuit current and resistor power vs time
i(t) = \frac{V_{final} - V_{initial}}{R}\, e^{-t/\tau} \qquad P_R(t) = i(t)^2 R
Settling, rise and half-voltage times
t_{settle} = 5\tau,\quad t_{10-90} = 2.197\,\tau,\quad t_{20-80} = \ln(4)\,\tau,\quad t_{1/2} = \tau \ln 2
Cutoff frequency
f_c = \frac{1}{2\pi R C}
Peak transient current and charge transferred
I_{peak} = \frac{|V_{final} - V_{initial}|}{R} \qquad \Delta Q = C\,|V_{final} - V_{initial}|
Energies and average resistor power
W_C = \tfrac{1}{2} C V_{final}^2,\quad W_R = \tfrac{1}{2} C (V_{final} - V_{initial})^2,\quad P_{R,avg} = C V_{in}^2 f_{cycle}
Impedance and low-pass response at frequency f
X_C = \frac{1}{2\pi f C},\quad |Z| = \sqrt{R^2 + X_C^2},\quad \theta = -\arctan\!\left(\frac{X_C}{R}\right),\quad A = \frac{1}{\sqrt{1 + (f/f_c)^2}}

Frequently asked questions

Do I have to enter a supply voltage?

No. The time constant, settling time, cutoff frequency and rise times only need R and C. But without Vin the calculator cannot show current, energy, or real voltage values, and the chart switches to a normalized scale from 0 to 1.

Why does the field I am solving for turn purple and say auto?

That box is the answer box. The calculator fills it in for you, so you should leave it alone and type in the other two. Click a different Solve for button, or just start typing in another field, and the target moves.

What shorthand can I type into the value boxes?

Type a number with one SI letter after it, like 22k, 3.3M, 47u, 100n, or 10p. The letter overrides the unit menu next to the box.

Codes with the letter in the middle, like 4k7, do not work. Type 4.7k instead.

Why does the calculator say INFEASIBLE?

It means the numbers you gave cannot exist in a real circuit. Common causes:

  • An initial voltage higher than Vin in charge mode
  • An initial voltage of 0 in discharge mode
  • A zero or negative R, C or τ

Fix the flagged input and the badge clears.

Why is my peak current so large?

At the very first instant the capacitor acts like a short circuit, so the only thing limiting current is R. Peak current equals the voltage step divided by R. A small resistor with a big capacitor makes a huge spike, even if the average current is tiny.

Enter your switch or diode current rating in Advanced Options to get a warning when the spike is too big.

What is the difference between rise time and the time constant?

The time constant is one exponential step. Rise time is what you measure on a scope: how long the signal takes to go from 10% to 90% (about 2.2τ) or from 20% to 80% (about 1.39τ).

Use τ for math and rise time when you compare against a datasheet or scope reading.

What do E12 and E24 mean in the standard values table?

They are the standard part value lists that factories actually make. E12 has 12 steps per decade (1.0, 1.2, 1.5 …) and E24 has 24 steps, so E24 is finer.

The table shows the closest real part above and below your ideal value, plus how much your τ shifts if you use it.

How do I pick R and C to hit a target time constant?

Enter your target in the Target Time Constant box. The tool tells you the C you need if R stays fixed, and the R you need if C stays fixed.

In practice, pick the capacitor first since caps come in fewer values, then choose the resistor to trim τ.

Does this calculator include ESR, leakage, or wire resistance?

No. It uses an ideal resistor and an ideal capacitor. Real parts add series resistance (ESR), leakage current, and wiring resistance, which make measured results a little slower or lossier.

Add the extra resistance into your R value if you want a closer match.

How do I use the time cursor on the chart?

Click the chart area once, then press the left and right arrow keys to step the cursor along the curve. Home jumps to t = 0 and End jumps to 5τ. The line under the chart shows voltage, current and resistor power at that moment.

Why does the Y-axis say norm instead of volts?

That happens when Vin is blank or zero. The chart then plots the shape of the curve from 0 to 1 instead of real units. Enter a supply voltage and the axes switch to volts, amps and watts.

What does Both mode show?

Both draws a charge curve and a discharge curve on the same chart so you can compare them. Peak current and resistor energy then report the worst case of the two events.

How do I size a bleed resistor for safety?

Enter a value in the Bleed Resistor box. The tool shows the bleed time constant, the time to reach 1% residual charge (5τ), and the time to fall under 50 V, which is the usual safe-touch limit.

It also shows the steady power the bleed resistor burns, so you can pick a big enough part.

Why does average resistor power matter?

One charge pulse is small, but a circuit that cycles thousands of times a second adds those pulses up fast. Enter your cycle frequency and the tool gives the average watts the resistor must handle. Pick a resistor rated above that number.

What is charge transferred (ΔQ)?

It is the amount of charge, in coulombs, that moves in or out of the capacitor during the transient. It equals C × the voltage change. It is useful for sizing a charge pump, a sample-and-hold input, or a battery-backed hold circuit.

My measured time constant does not match the calculator. Why?

Usually part tolerance. A ±10% resistor with a ±20% capacitor can shift τ by roughly 30% in the worst case. Enter both tolerances in Advanced Options to see the real range.

Class II ceramics (X5R, X7R, Y5V) also lose capacitance under DC bias, which makes the circuit faster than the label suggests.

Is 5τ always enough settling time?

For most digital and power work, yes — 5τ leaves under 1% error. Precision jobs need longer: about 6.9τ for 0.1% and 9.2τ for 0.01%. Pick Sample-and-Hold under Application Context to see those numbers for your circuit.

Can I use this for an RL circuit?

No. This tool solves RC only. An inductor circuit uses τ = L / R, which is a different formula, though the exponential curve shape is the same.

What is the cutoff frequency good for?

It is the −3 dB corner of an RC filter. Signals below it pass through a low-pass filter; signals above it get cut. At that exact frequency the capacitor's reactance equals R, and the output drops to about 70.7% of the input.

Why do I get a voltage margin warning when my cap rating is higher than Vin?

The warning fires when Vin sits within 10% of the rating. That is too tight for real use because of ripple, spikes, and aging. Most designers derate: run electrolytics near 80% of rated volts and tantalums near 50%.

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