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Electrical calculator

RC Time Constant Calculator

Calculate the RC time constant τ = R×C, solve for R or C, and get −3 dB frequency plus 2.2τ / 5τ timing estimates. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 3/3 declared partitions (solve-tau, solve-C, invalid-domain) · Matrix
Known limitations
  • First-order RC only
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Series RC time constant and solved R/C/τ, plus ideal LPF −3 dB frequency and 2.2τ / 5τ timing multiples.
Scope
Lumped series first-order RC.
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
7/7 property · digest c2ad16b2e943
Legacy regression
16/16 tests · Production surface contract 3/3
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
3/3 golden · 6/6 CVP boundary · 4/4 invalid · 7/7 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • IEC 60050 — International Electrotechnical Vocabulary — Time constant of an exponential quantity
  • Horowitz & Hill — The Art of Electronics — RC circuits, time constants, and single-pole filters
  • NIST Guide to the SI (SP 811) — SI units for resistance, capacitance, and time
Sources
Evidence
3 legacy golden · 6 legacy boundary · legacy regression suite · 3/3 oracle-backed golden · 4/4 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Time constantτ = R × C
Solve CC = τ ÷ R
Solve RR = τ ÷ C
−3 dB frequencyf_c = 1 ÷ (2π R C)
10%–90% rise (approx.)t₁₀₋₉₀ ≈ 2.2 τ
Settling horizont₅τ = 5 τ
iUse SI units in the API: ohms, farads, seconds. The UI accepts common engineering prefixes (kΩ, µF, ms). f_c is for an ideal series-R / shunt-C low-pass; high-pass and multi-order networks differ.

How to use

1

Enter any two of R, C, τ

Leave the unknown blank. If R and C are both filled, τ is computed from R×C.

2

Read τ and derived timings

Result includes f_c, ≈2.2τ rise, and 5τ settling.

3

Check units

1 µF = 1×10⁻⁶ F; 10 kΩ = 10000 Ω; 1 ms = 0.001 s.

Example calculations

Common configurations with formula and result.

ϟ

Classic RC

10 kΩ · 1 µF

τ = 10000 × 1e-6
τ = 10 ms · f_c ≈ 15.915 Hz
ϟ

Solve C from τ

R = 4.7 kΩ · τ = 1 ms

C = 0.001 / 4700
C ≈ 212.8 nF
ϟ

Solve R from τ

C = 100 nF · τ = 47 µs

R = 47e-6 / 100e-9
R = 470 Ω
ϟ

Rise-time estimate

τ = 10 ms

2.2τ
t₁₀₋₉₀ ≈ 22 ms

Common RC pairs

Common values at a glance.

RCτf_c (approx.)
10 kΩ1 µF10 ms15.9 Hz
1 kΩ100 nF100 µs1.59 kHz
4.7 kΩ10 nF47 µs3.39 kHz
100 kΩ100 nF10 ms15.9 Hz
i f_c = 1/(2πRC) for ideal first-order LPF.

RC Time Constant calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-08

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
The RC time constant τ = R × C is the characteristic time of a series resistor–capacitor network. After one τ, a step response reaches about 63.2% of its final value. This calculator solves any two of R, C, and τ, and reports the ideal first-order LPF −3 dB frequency and common timing multiples.
What it calculates
Series RC time constant and solved R/C/τ, plus ideal LPF −3 dB frequency and 2.2τ / 5τ timing multiples.
Inputs
  • Any two of R (Ω), C (F), tau (s); each provided value must be > 0
Outputs
  • R, C, tau
  • f_c = 1/(2πRC) (Hz)
  • t_10_90 ≈ 2.2τ (s)
  • t_5tau = 5τ (s)
Formula
τ=R·C; f_c=1/(2πRC); t₁₀₋₉₀≈2.2τ; t₅τ=5τ
Assumptions
  • Lumped series first-order RC.
  • When R and C are both given, tau is taken as R·C.
Units
  • Ω, F, s → Hz
Boundary conditions
  • Fewer than two inputs → NEEDS_TWO_INPUTS
  • Non-finite → INVALID_NUMBER
  • ≤ 0 → VALUE_MUST_BE_POSITIVE
Example
R=10 kΩ, C=1 µF → τ=10 ms, f_c≈15.915 Hz
Validation cases

6 published on this page · 16/16 tests · Production surface contract 3/3 · View evidence

  • R=10000, C=1e-6 → tau=0.01, f_c≈15.9155
  • R=4700, tau=0.001 → C≈2.1277e-7
  • C=1e-7, tau=4.7e-5 → R=470
  • only R → error NEEDS_TWO_INPUTS
  • R=0, C=1e-6 → error VALUE_MUST_BE_POSITIVE
  • R=nan, C=1e-6 → error INVALID_NUMBER
Sources
  • IEC 60050 — International Electrotechnical Vocabulary — Time constant of an exponential quantity
    Supports: τ definition for exponential RC response
  • Horowitz & Hill — The Art of Electronics — RC circuits, time constants, and single-pole filters
    Supports: τ = RC; ≈2.2τ for 10%–90%; f_c = 1/(2πRC)
  • NIST Guide to the SI (SP 811) — SI units for resistance, capacitance, and time
    Supports: Ω, F, s as coherent units for τ = RC
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Solve the RC time constant τ = R × C from any two of R, C, and τ, and read ideal −3 dB frequency plus 2.2τ / 5τ timing estimates.

Default example: 10 kΩ · 1 µF → τ = 10 ms, f_c ≈ 15.915 Hz.

Supported and not supported

Supported

  • Series first-order RC: solve any two of R, C, τ
  • Ideal LPF corner f_c = 1/(2πRC)
  • Approximate 10%–90% rise ≈ 2.2τ and settling horizon 5τ
  • API result { R, C, tau, f_c, t_10_90, t_5tau } via electrical.rc_time_constant

Not supported

  • Parallel / multi-order / distributed RC networks
  • Full transient simulation with arbitrary drive waveforms
  • RLC resonance (see upcoming RLC tool)
  • Op-amp active filters or switched-capacitor networks

Agent / API notes

Capability id: electrical.rc_time_constant · tool id: rc-time-constant · pin calculation_version: 1.0.0.

Stable error codes: NEEDS_TWO_INPUTS, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE.

Inputs are SI: R in ohms, C in farads, tau in seconds.

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Frequently asked questions

Key distinctions behind the calculation.

What is the RC time constant?

τ = R×C. It is the time for the capacitor voltage in a series RC step response to reach about 63.2% of its final value (or to fall to about 36.8% when discharging).

How many time constants to settle?

A common rule of thumb is ~5τ to reach about 99.3% of the final value for a first-order exponential. This tool reports t_5tau = 5τ as that horizon.

What is 2.2τ?

For a single-pole RC step, the 10%–90% rise time is approximately 2.2τ. It is an estimate, not a full transient simulator.

What units should I use?

API inputs are SI: R in ohms, C in farads, tau in seconds. The page UI converts kΩ/MΩ, nF/µF/mF, and µs/ms/s for convenience.

What if I only enter one value?

The calculator and API reject the request with NEEDS_TWO_INPUTS. Provide any two of R, C, and tau.

Is f_c for high-pass or low-pass?

The reported f_c = 1/(2πRC) is the −3 dB corner of the ideal series-R / shunt-C low-pass. A high-pass (series-C / shunt-R) shares the same magnitude corner formula but swaps which band passes.