# [RC Time Constant Calculator](https://blog.hirnschall.net/tools/rc-time-constant/)

author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/)

meta description: Calculate the RC time constant. Solve for τ, resistance, or capacitance given the other two. Optionally calculate charging or discharging voltage at any time t.

meta title: RC Time Constant Calculator — Solve for τ, R, or C

date published: 01.04.2025 (DD.MM.YYYY format)
date last modified: 22.04.2025 (DD.MM.YYYY format)

---

Calculator
----------

Provide any two of \( R \), \( C \), \( \tau \) — the third is solved. Optionally provide a time \( t \) and an initial or supply voltage to calculate the charging or discharging voltage at that time.

* Resistance (R):
* Ω
  kΩ
  MΩ

* Capacitance (C):
* F
  mF
  µF
  nF
  pF

* Time constant (τ):
* s
  ms
  µs
  min

---

* Time (t) — optional:
* s
  ms
  µs
  min

* Supply voltage Vs (charging) — optional:
* V
  mV
  kV

* Initial voltage V0 (discharging) — optional:
* V
  mV
  kV

Provide any two of R, C, τ to calculate.

Calculate



RC Time Constant — Explanation
------------------------------

The RC time constant \( \tau \) characterises how quickly a capacitor charges or discharges through a resistor:
\[
\tau = R \cdot C
\]
Where \( R \) is in Ohms and \( C \) is in Farads, giving \( \tau \) in seconds. It is the single most important parameter of any RC circuit — it sets the speed of every transition.

Charging
--------

When a discharged capacitor is connected to a supply voltage \( V\_s \) through a resistor, the voltage across the capacitor rises exponentially:
\[
V(t) = V\_s \cdot \left(1 - e^{-t/\tau}\right)
\]
After one time constant the capacitor has charged to \( 1 - 1/e \approx 63.2\% \) of \( V\_s \). After five time constants it is considered fully charged:
\[
\begin{align}
t = 1\tau &\Rightarrow V = 63.2\%\ V\_s \\
t = 2\tau &\Rightarrow V = 86.5\%\ V\_s \\
t = 3\tau &\Rightarrow V = 95.0\%\ V\_s \\
t = 4\tau &\Rightarrow V = 98.2\%\ V\_s \\
t = 5\tau &\Rightarrow V = 99.3\%\ V\_s
\end{align}
\]

Discharging
-----------

When a fully charged capacitor discharges through a resistor, the voltage decays exponentially:
\[
V(t) = V\_0 \cdot e^{-t/\tau}
\]
After one time constant the voltage has dropped to \( 1/e \approx 36.8\% \) of \( V\_0 \). The decay is the mirror image of the charging curve.

Purpose of the Calculator
-------------------------

Given any two of \( R \), \( C \), \( \tau \), the calculator solves for the third:

* To solve for \( \tau \): \[ \tau = R \cdot C \]
* To solve for \( R \): \[ R = \frac{\tau}{C} \]
* To solve for \( C \): \[ C = \frac{\tau}{R} \]

Optionally, providing \( t \) and \( V\_s \) or \( V\_0 \) calculates the charging or discharging voltage at that time. Both can be provided simultaneously to compare charging and discharging in the same circuit.

More info
---------

Looking for more helpful tools and calculators? Explore a wide range of resources to simplify your engineering projects and calculations. Head over to our [tools section](https://blog.hirnschall.net/tools/) to find our free online calculators.  
For actual projects and informational articles head over to [blog.hirnschall.net](https://blog.hirnschall.net/).