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Time constant calculator

A-level Electricity

The time constant of a resistor and capacitor circuit. After one time constant a discharging capacitor has 37% of its starting charge.

τ = R C

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

τTime constant to find 4.70 s

RResistance

CCapacitance

Significant figures

Working

Write the equation
τ = R C
Substitute the values
τ = 47000 × (1 × 10⁻⁴)
Calculate
τ = 4.7 s
Give the answer to 3 significant figures
τ = 4.70 s

Worked example

Find τ, the time constant. Given: resistance R = 47000 Ω; capacitance C = 1.00 × 10⁻⁴ F.

Write the equation
τ = R C
Substitute the values
τ = 47000 × (1 × 10⁻⁴)
Calculate
τ = 4.7 s
Give the answer to 3 significant figures
τ = 4.70 s

Symbols and units

Symbol	Quantity	SI unit
τ	Time constant	s
R	Resistance	Ω
C	Capacitance	F

Time constant: rearranged

To find time constant: τ = R C
To find resistance: R = τ / C
To find capacitance: C = τ / R

Exam tip

Use ohms and farads and the answer is in seconds. After about five time constants it is close to fully discharged.

Common questions

What is the formula for time constant?

The equation is τ = R C, where τ is the time constant (s); R is the resistance (Ω); C is the capacitance (F).

What units should I use for time constant?

In SI units: time constant in s, resistance in Ω, capacitance in F. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange τ = R C?

Rearranging gives these forms: to find time constant: τ = R C. to find resistance: R = τ / C. to find capacitance: C = τ / R.

Practise time constant questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Read the full explanation on the Capacitor time constant formula page. More electricity equations: Charge, current and time, Ohm’s law, Electrical power, Electrical power, Energy transferred, Resistors in series, Resistors in parallel, Resistivity. See the full list on the a-level physics equation calculator page.