How to use the RC Time Constant Calculator
- 1. Enter R and CType values like 10k and 100u (100 µF).
- 2. Charging or dischargingPick the case and add the supply voltage.
- 3. Read τ and VcOptionally enter a time to get the exact capacitor voltage then.
RC charging and discharging formulas
The time constant is τ = R × C (ohms × farads = seconds). While charging from 0 V towards Vs, Vc(t) = Vs (1 − e−t/τ). While discharging from V0, Vc(t) = V0 e−t/τ. The current in both cases is (V/R) e−t/τ.
After 1τ the capacitor reaches 63.2% of the final voltage, after 2τ 86.5%, 3τ 95.0%, 4τ 98.2% and 5τ 99.3%. Engineers treat 5τ as fully charged.
Worked example: R = 10 kΩ, C = 100 µF, Vs = 5 V. τ = 10,000 × 0.0001 = 1 s. At t = 1 s, Vc = 5 × (1 − e−1) = 3.16 V. It is practically full after 5 s.
Where it shows up in exams
- Find the time for a capacitor to charge to a given voltage: t = −τ ln(1 − Vc/Vs).
- Find the voltage after a given time while discharging.
- Relate τ to the cut-off frequency of a first-order filter: fc = 1 / (2πRC).
- Design a power-on reset or switch debounce delay.
The half-way time, 0.693τ, is the same ln 2 factor you see in the 555 timer formulas.
Frequently asked questions
What is one time constant?
It is the time for the capacitor to reach 63.2% of its final charge, or to drop to 36.8% while discharging. It equals R × C.
Why is 5τ called fully charged?
At 5τ the capacitor is at 99.3% of the final voltage. The rest is too small to matter in most circuits, though in theory it never reaches 100%.
Does the supply voltage change τ?
No. τ depends only on R and C. The voltage only scales the curve.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.