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RC Time Constant Calculator

τ = R C. 10 kΩ and 100 µF is 1 s; E = 1.25 mJ.

By Jasper · Updated

Calculator

PASS1 sE 1.25 mJ

τ = R C. Charge Vc(t) = V (1 − e^(−t/τ)); discharge V e^(−t/τ). Energy uses V².

τ
1 s
E
1.25 mJ
fc
0.1592 Hz
  • Pass Stored energy: E = ½ C V² = 0.00125000 J
  • Pass Time constant: τ = RC = 1.00000 s

Formula

Time constant

τ=RC τ = R C

Charging exponential

Vc(t)=V(1-e-t/τ) Vc(t) = V (1 − e^(−t/τ))

Stored energy

E=12CV2 E = ½ C V²

Variables

Symbol Meaning Unit Typical range Precision Default
R Resistance Ω ≥ 0 mΩ 4 sig 10 kΩ
C Capacitance F ≥ 0 pF 4 sig 100 µF
V Voltage V — 4 sig 5 V
tau Time constant s — 4 sig —
E Stored energy J — 4 sig —
Q Charge — — 4 sig —
fc Cutoff frequency Hz — 4 sig —

Worked example

10 kΩ, 100 µF, 5 V

Input Value
R · Resistance 10 kΩ
C · Capacitance 100 µF
V · Voltage 5 V
Output Value
tau · Time constant 1 s
E · Stored energy 1.25 mJ
Q · Charge 0.0005
fc · Cutoff frequency 0.1592 Hz

1 MΩ, 1 µF, 12 V

Input Value
R · Resistance 1 MΩ
C · Capacitance 1 µF
V · Voltage 12 V
Output Value
tau · Time constant 1 s
E · Stored energy 72 µJ

How it works

Most reset pins, analog RC filters and one-shots come down to τ = R C. The exponential is the same curve every time; this page prints 1τ through 5τ so you do not have to reach for a table.

Enter R, C and V. Energy and charge are reported even if you only care about timing. For 555 thresholds, use the 555 timer calculator instead of this generic exponential.

Pitfalls

  • Leaving C in microfarads without converting — 100 in the F field is 100 F, not 100 µF.
  • Using 2.2 τ as exact 90 % without checking the exponential. This table lists 1τ…5τ exactly.
  • Ignoring that a GPIO pin adds series resistance not in your τ.

FAQ

What is τ for 10 kΩ and 100 nF?

1 ms. Scale R or C linearly.

How much voltage at 1τ on a charge?

About 63.2 % of V. Discharge is 36.8 % remaining.

What is the cutoff frequency?

fc = 1 / (2π R C) for the first-order low-pass.

Can V be negative?

Yes. Energy uses V²; the table voltages keep the sign.

Related

Sources