RC & RL Time Constant Calculator
A 10 kΩ resistor with a 100 µF capacitor has a time constant of 1 s: after one τ the capacitor has charged to 63.2 % of the supply.
1 s
- Capacitor voltage at t = 1 s
- 6.321205588 V
- Current at t
- 0.0003678794412 A
- Fraction of the final value
- 63.21205588 %
- Time to 99 % (4.605 τ)
- 4.605170186 s
- Practically settled (5 τ)
- 5 s
Step-by-step solution
- τ = R × C = 10000 Ω × 0.0001 F = 1 s
- t/τ = 1 ÷ 1 = 1; e^(−t/τ) = 0.3678794412
- v_C = V(1 − e^(−t/τ)) = 10 × 0.6321205588 = 6.321205588 V
RC & RL Time Constant Formula
τ = RC, v_C(t) = V(1 − e^(−t/τ))
RL circuit: τ = L/R, i(t) = (V/R)(1 − e^(−t/τ)); discharging uses e^(−t/τ)
Worked Example
A 10 kΩ resistor charging a 100 µF capacitor from 10 V, after 1 s:
- τ = R × C = 10000 Ω × 0.0001 F = 1 s
- t/τ = 1 ÷ 1 = 1; e^(−t/τ) = 0.3678794412
- v_C = V(1 − e^(−t/τ)) = 10 × 0.6321205588 = 6.321205588 V
Current at t: 0.0003678794412 A · Fraction of the final value: 63.21205588 % · Time to 99 % (4.605 τ): 4.605170186 s · Practically settled (5 τ): 5 s
GATE tip
For a switched circuit, find the Thevenin resistance seen by the capacitor or inductor with sources turned off: τ = R_Th C or L/R_Th. Then x(t) = x(∞) + [x(0⁺) − x(∞)] e^(−t/τ) solves almost every first-order GATE question.
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Frequently asked questions
Why 63.2 % after one time constant?
Because 1 − e⁻¹ = 0.632. After 2τ it reaches 86.5 %, after 3τ 95 %, and after 5τ 99.3 %, which engineers treat as fully charged.
What is the time constant of an RL circuit?
τ = L/R. A 10 mH inductor with 10 kΩ has τ = 1 µs; the current rises to 63.2 % of V/R in that time.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). RC & RL Time Constant Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/rc-time-constant-calculator/
IEEE
Scientific Converters, "RC & RL Time Constant Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/rc-time-constant-calculator/