Skip to content
Free calculators and practical guides for smarter home projects.
DIY Cost Tools

DIY Cost Tools

RC Time Constant Calculator

Estimate the timescale of an ideal resistor-capacitor transient. The charging and discharging outputs represent two separate initial conditions. Charging begins with an uncharged capacitor and a step to the supply voltage. Discharging begins at the entered initial voltage with the supply removed from the ideal discharge path. Five time constants is a useful reference point, not a claim that all remaining charge has vanished.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the units and positive-value requirements below.

Time constant τ (s)1
Five time constants (s)5
Charging voltage at time t (V)7.585446706
Discharging voltage at time t (V)4.414553294

How to use this calculator

  1. Match your inputs to the stated circuit model and field labels.
  2. Convert your quantities to the units printed next to each field.
  3. Select Calculate, or press Enter, and read the labeled results.

Formula and method

τ = RC; charging from zero: VC(t) = Vs(1 − e⁻ᵗ/τ); discharging from V0: VC(t) = V0e⁻ᵗ/τ.

The calculation runs in your browser. After changing an input, select Calculate again. Invalid inputs or undefined mathematical conditions hide the previous result so it cannot be mistaken for an answer to the new values.

Worked example

For 10,000 Ω and 100 µF, τ = 1 s. At t = 1 s and 12 V, the charging voltage is approximately 7.585446706 V; a separate discharge starting at 12 V gives approximately 4.414553294 V.

Limitations and safety

Ideal-component calculation only. Component tolerance, heating, parasitic effects and frequency limits are not modeled. This output does not establish component ratings, wiring compliance or a safe circuit design. Have consequential designs checked by a qualified professional; do not use this tool as instructions for working on energized equipment. Source resistance, leakage and nonzero charging initial voltage are excluded. Discharge calculations do not prove a capacitor safe to touch.

The fields accept signed numerical input, but positive-only component values and nonnegative time or frequency requirements are enforced by the calculation. Read each error message before changing a value. Results use floating-point arithmetic and are shown to approximately 10 significant digits; component tolerances generally do not justify using all those digits in a physical design.

Frequently asked questions

Is a capacitor fully charged or discharged after 5τ?

No. The remaining exponential fraction is e⁻⁵, about 0.674%. Real circuits can behave differently.

Why are my units important?

The calculator uses exactly the units printed in the input labels. For example, a micro-unit is one millionth of a base unit, and a milli-unit is one thousandth. Entering a base-unit value into a prefixed-unit field changes the meaning of the input.

Does the answer establish a safe component rating?

No. The formula evaluates an ideal model. Ratings, tolerances, transients, installation requirements and environmental limits need a separate design assessment.

Review notes and reference

Reviewed October 3, 2026. The default worked example and an additional boundary or scaling check were tested against expected values. Validation checks included blanks, nonnumeric text and inputs outside the supported range. OpenStax University Physics formula reference provides the circuit theory behind this model. The text and worked example on this page are original.

Related calculators

Electrical calculators · Voltage Divider Calculator · Resistor Network Calculator · Capacitor Energy Calculator · Ohm’s Law Calculator · All calculators