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RC Circuit Calculator

Calculate RC time constant, cutoff frequency, charge/discharge timing, filter gain, impedance, and resistor or capacitor values from target τ or cutoff.

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RC circuit calculator Calculate RC time constant, cutoff frequency, charge and discharge timing, low-pass or high-pass gain, impedance, and practical tolerance bands. You can also design the missing resistor or capacitor from a target time constant or cutoff frequency.

Mode

Reference presets

Filter output

Result

1 ms

10 kΩ with 100 nF gives τ 1 ms, cutoff 159.1549 Hz, and 5τ settling near 5 ms.

RC time constant
1 ms
5τ settling near 5 ms
Cutoff frequency
159.1549 Hz
-3 dB corner
Selected filter gain
0.707
-3.01 dB at 159.15 Hz
Charge at elapsed time
63.21%
discharge remains 36.79%
Series impedance
14.1424 kΩ
phase -45°
Target charge time
2.3026 ms
to 90% charged
10-90% rise time
2.1972 ms
about 2.2τ

Component values

10 kΩ with 100 nF. 10 kΩ and 100 nF.

Tolerance band

With ±15% combined tolerance, τ can range from 850 µs to 1.15 ms and cutoff from 138.3956 Hz to 187.2411 Hz.

Filter comparison

Low-pass gain is 0.707 (-3.01 dB); high-pass gain is 0.707 (-3.01 dB).

Charge voltage
3.1606 V
Discharge voltage
1.8394 V
Initial current
500 µA
Current at elapsed time
183.9397 µA
Stored energy
1.25 µJ

Milestone curve checkpoints

Use the 1τ, 3τ, and 5τ checkpoints to estimate charging and discharging progress without plotting the full exponential curve.

1τ

Time: 1 ms

Charge: 63.21%

Discharge: 36.79%

3τ

Time: 3 ms

Charge: 95.02%

Discharge: 4.98%

5τ

Time: 5 ms

Charge: 99.33%

Discharge: 0.67%

Equations used

τ = R × C = 10000 Ω × 1e-7 F = 1 ms

fc = 1 / (2πRC) = 159.1549 Hz

Using entered R and C values.

Charge fraction = 1 - e-t/τ; discharge fraction = e-t/τ; fc = 1 / (2πRC); Xc = 1 / (2πfC).

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Basic circuits

RC circuit calculator: time constant, cutoff, charge, discharge, and filter design

An RC circuit calculator helps translate one resistor-capacitor pair into timing, filter, and impedance behaviour you can act on. This version solves the RC time constant, cutoff frequency, charge and discharge progress, 5τ settling time, 10-90% rise time, target-charge timing, low-pass or high-pass gain, and series impedance. It can also design the missing resistor or capacitor from a target time constant or cutoff frequency.

What this RC circuit calculator covers

This page treats the network as one ideal first-order resistor-capacitor pair. It calculates the RC time constant, cutoff frequency, capacitive reactance, series impedance, exponential charge-discharge progress, selected low-pass or high-pass gain, and common timing checkpoints.

The calculator also supports design workflows that many basic RC time constant calculators skip. If you know the target time constant, it can solve the missing capacitor from a fixed resistor or the missing resistor from a fixed capacitor. If you know the target cutoff frequency, it uses the same relationship to size the missing component for a first-order RC filter.

An optional supply voltage converts the normalized timing result into actual charge voltage, discharge voltage, current, and stored-energy context. Optional tolerance inputs show a practical range for time constant and cutoff frequency, which is important because real capacitors often have wider tolerances than precision resistors.

The time constant sets the pace of the curve

The RC time constant tells you how quickly the network moves through its exponential charge and discharge response. One time constant means the charging capacitor has reached about 63.2% of final value and the discharging capacitor has about 36.8% of its starting value left.

Those checkpoints are useful because they let you estimate timing without plotting the full curve every time. Around 3τ, a charging capacitor is near 95% of final value. Around 5τ, it is close enough to final value for many practical timing discussions, although mathematically the exponential curve approaches the final value asymptotically.

The calculator also reports 10-90% rise time because digital, control, and measurement discussions often care about the time it takes to move through the useful middle of the transition rather than the first 63.2% point alone.

τ = R × C

Resistance multiplied by capacitance gives the characteristic timing constant of the RC pair.

Charge fraction = 1 - e^(-t/τ); discharge fraction = e^(-t/τ)

These exponential forms determine the charge and discharge percentage at any stated time.

10-90% rise time ≈ 2.2τ

The calculator uses ln(9) × τ for the 10% to 90% interval.

Cutoff frequency connects the same RC pair to filter response

The same R and C values that set timing also define the cutoff frequency. For a first-order low-pass or high-pass RC filter, the cutoff frequency is fc = 1 / (2πRC). At that frequency, the ideal output magnitude is about 0.707 of the passband value, which corresponds to the familiar -3 dB point.

A low-pass output is normally taken across the capacitor, so it passes slower changes and attenuates faster changes. A high-pass output is normally taken across the resistor, so it blocks DC and low-frequency content while passing faster changes. The cutoff formula is the same; the output node determines whether the response is low-pass or high-pass.

The calculator reports both low-pass and high-pass gain at the chosen analysis frequency, then highlights the selected filter type. This helps avoid a common mistake: using the right cutoff frequency formula but interpreting the wrong output node.

fc = 1 / (2πRC)

The RC pair's cutoff frequency is the reciprocal of 2πRC.

Xc = 1 / (2πfC); |Z| = √(R² + Xc²)

Capacitive reactance and series impedance describe the same pair in the frequency domain.

Designing from a target time constant or cutoff frequency

When the design requirement is stated as a delay, choose the design-from-τ mode. Keeping the resistor fixed solves C = τ / R. Keeping the capacitor fixed solves R = τ / C. This is useful for debounce circuits, delay networks, reset timing, simple pulse shaping, and first-pass 555-adjacent timing checks.

When the design requirement is stated as a filter corner, choose the design-from-cutoff mode. Keeping the resistor fixed solves C = 1 / (2πfR). Keeping the capacitor fixed solves R = 1 / (2πfC). This is useful for low-pass smoothing, AC coupling, high-pass input protection, tone shaping, and simple anti-noise filtering.

The design outputs are ideal values. In real circuits, you usually choose the nearest standard component value and then recalculate the actual τ and fc. That is why the calculator keeps the solved component, recalculated timing, cutoff, gain, and tolerance range visible together.

C = τ / R; R = τ / C

Rearranged time-constant formulas for component sizing.

C = 1 / (2πfR); R = 1 / (2πfC)

Rearranged cutoff-frequency formulas for first-order RC filter design.

Worked examples

Example 1: 10 kΩ and 100 nF gives τ = 0.001 s, or 1 ms. The cutoff frequency is about 159.15 Hz. At 1 ms, the charging curve is 63.2% of final voltage and the discharge curve is 36.8% of its starting voltage.

Example 2: if the target time constant is 1 s and the fixed resistor is 100 kΩ, the required capacitance is C = 1 / 100,000 = 10 µF. If the supply is 5 V, the capacitor reaches about 3.16 V after one time constant and about 4.97 V after five time constants.

Example 3: if the target cutoff is 2 kHz and the fixed capacitor is 10 nF, the required resistance is about 7.96 kΩ. The same pair has a time constant of about 79.6 µs, and either the low-pass or high-pass output is around -3 dB at the cutoff frequency.

How to interpret tolerance and practical circuit limits

Ideal RC math assumes exact components. Real components have tolerances, temperature coefficients, leakage, equivalent series resistance, and layout parasitics. A 1% resistor paired with a 20% capacitor can move the time constant much more than the resistor alone would suggest.

The tolerance range in the calculator is a first-pass worst-case estimate using the entered resistor and capacitor tolerances. It does not replace a datasheet review or a circuit simulation, but it makes the likely direction of drift visible before you pick parts.

Long time constants are especially sensitive to leakage current, PCB contamination, input bias current, and capacitor type. High-frequency filters are more sensitive to layout, source impedance, load impedance, and parasitic capacitance or inductance. In those cases, validate the design against the actual circuit rather than relying only on the ideal RC result.

What this calculator does not model

This calculator is for one ideal first-order RC pair. It does not model source impedance, load impedance, diode paths, op-amp buffering, component ESR, dielectric absorption, leakage, PCB parasitics, or multi-pole filter topologies.

Use it as a planning and educational reference. If the real circuit includes multiple poles, switching behaviour, high-voltage safety, pulse-current stress, or performance-critical frequency response, move to a simulation or measurement workflow that captures those effects explicitly.

The page is universal rather than country-specific. It uses SI electrical units and does not apply jurisdictional wiring rules or product-safety standards.

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Frequently asked questions

What does one RC time constant really mean?

At one τ, the charging capacitor has reached about 63.2% of its final voltage and a discharging capacitor has about 36.8% of its original voltage left. It is the basic timing marker for an ideal first-order RC circuit.

How many time constants does it take to fully charge a capacitor?

A capacitor never becomes mathematically 100% charged in the ideal exponential model, but 5τ is commonly treated as practically complete because the charging voltage is about 99.3% of final value. The calculator shows 1τ, 3τ, and 5τ checkpoints so you can choose the level of settling that fits the job.

What is the cutoff frequency of an RC circuit?

For an ideal first-order RC low-pass or high-pass filter, cutoff frequency is fc = 1 / (2πRC). It is the -3 dB corner where the ideal output magnitude is about 0.707 of the passband value.

Can I use the same cutoff formula for low-pass and high-pass RC filters?

Yes. The same R and C determine the cutoff frequency. The difference is where the output is taken: across the capacitor for a basic low-pass response, or across the resistor for a basic high-pass response.

How do I choose a resistor and capacitor for a target cutoff frequency?

Fix one component first, then solve the other. If the resistor is fixed, use C = 1 / (2πfR). If the capacitor is fixed, use R = 1 / (2πfC). After choosing the nearest standard value, recalculate the actual cutoff frequency.

How do I choose a resistor and capacitor for a target delay?

Use the time constant formula τ = RC. If the resistor is fixed, C = τ / R. If the capacitor is fixed, R = τ / C. Then decide whether the circuit needs 1τ, 3τ, 5τ, or a specific charge percentage before treating that delay as finished.

Why does the calculator show 10-90% rise time?

Many timing and measurement discussions use 10-90% rise time rather than one time constant. For an ideal first-order RC response, the 10-90% rise time is ln(9) × τ, which is about 2.2τ.

Does component tolerance affect the RC result?

Yes. Since τ = R × C, resistor and capacitor tolerances both move the time constant. The cutoff frequency moves in the opposite direction because fc = 1 / (2πRC). Capacitor tolerance is often the larger contributor.

Why does the measured cutoff frequency differ from the calculator?

The ideal formula assumes an unloaded first-order network with exact components. Real measurements can shift because of source resistance, load resistance, capacitor ESR, probe capacitance, PCB parasitics, component tolerance, and frequency-dependent component behaviour.

Is this calculator for series or parallel RC circuits?

The calculator models one first-order RC pair for timing and simple filter analysis. The impedance result is the series RC magnitude at the chosen frequency. More complex parallel networks, loaded filters, and multi-stage filters need a dedicated model.

Can I use this for switch debouncing?

Yes as a first-pass timing estimate. Debounce circuits often use an RC low-pass effect, but the actual logic threshold, switch bounce pattern, input leakage, Schmitt trigger behaviour, and pull-up or pull-down arrangement also matter.

Can this replace circuit simulation?

No. It is a fast ideal RC calculator for first-pass timing and filter design. Use simulation or measurement when the circuit includes loading, multiple poles, active devices, switching paths, high voltage, safety constraints, or tight tolerance requirements.

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