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Low-Pass Filter Calculator

Design a first-order RC low-pass filter: solve any two of R, C, and cutoff fc = 1/(2πRC), and evaluate magnitude |H(f)| in linear and dB. 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 · 4/4 declared partitions (solve-rc, with-f, solve-C, invalid-domain) · Matrix
Known limitations
  • First-order RC LPF only
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
First-order RC LPF cutoff and optional magnitude response.
Scope
Ideal lumped series-R / shunt-C LPF.
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
4/4 property · digest 00b0f7286660
Legacy regression
10/10 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 · 3/3 CVP boundary · 3/3 invalid · 4/4 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • Horowitz & Hill — The Art of Electronics — Single-pole RC filters
  • IEC 60050 — IEV — Cut-off frequency
Sources
Evidence
3 legacy golden · 3 legacy boundary · legacy regression suite · 3/3 oracle-backed golden · 3/3 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.

Cutofffc = 1 / (2πRC)
Magnitude|H| = 1 / √(1+(f/fc)²)
iPassive first-order RC LPF only. For time-constant-centric solves see the RC time constant tool (τ = RC).

How to use

1

Enter any two of R, C, and fc

Leave the unknown blank to solve it. Values must be > 0.

2

Optional: enter evaluation frequency f

If provided, magnitude |H| and H_dB are shown at that frequency.

3

Read cutoff and response

fc = 1/(2πRC) for a first-order RC low-pass.

Example calculations

Common configurations with formula and result.

ϟ

10 kΩ · 1 µF

R=10 kΩ · C=1 µF

fc = 1/(2πRC)
fc ≈ 15.915 Hz · −3 dB at fc
ϟ

Solve C

R=4.7 kΩ · fc=1 kHz

C = 1/(2πRfc)
C ≈ 33.86 nF
ϟ

Attenuation at 10×fc

f = 10·fc

|H|_dB
≈ −20.04 dB

Low-Pass Filter 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
A first-order series-R / shunt-C low-pass filter has cutoff fc = 1/(2πRC). At f = fc the magnitude is −3.01 dB. Magnitude at any f is |H| = 1/√(1+(f/fc)²).
What it calculates
First-order RC LPF cutoff and optional magnitude response.
Inputs
  • Any two of R (Ω), C (F), fc (Hz) — each > 0
  • Optional f (Hz) > 0 for |H| and H_dB
Outputs
  • R, C, fc, tau=RC, omega_c=2πfc
  • Optional f, H_lin, H_dB
Formula
fc=1/(2πRC); |H|=1/√(1+(f/fc)²); H_dB=20·log10(|H|)
Assumptions
  • Ideal lumped series-R / shunt-C LPF.
  • When R and C are both given, fc is recomputed from them.
Units
  • Ω, F, Hz
Boundary conditions
  • Fewer than two of R/C/fc → NEEDS_TWO_INPUTS
  • ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Non-finite → INVALID_NUMBER
Example
R=10 kΩ, C=1 µF → fc≈15.915 Hz; at fc, H_dB≈−3.01 dB
Validation cases

5 published on this page · 10/10 tests · Production surface contract 3/3 · View evidence

  • R=10000, C=1e-6 → fc≈15.9155
  • R=10000, C=1e-6, f=fc → H_dB≈−3.0103
  • R=4700, fc=1000 → C≈3.386e-8
  • only R → error NEEDS_TWO_INPUTS
  • R=0, C=1e-6 → error VALUE_MUST_BE_POSITIVE
Sources
  • Horowitz & Hill — The Art of Electronics — Single-pole RC filters
    Supports: fc = 1/(2πRC); −3 dB at corner; −20 dB/decade
  • IEC 60050 — IEV — Cut-off frequency
    Supports: Definition of cutoff / corner frequency for filters
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Design a first-order RC low-pass: solve any two of R, C, and fc, and optionally evaluate |H(f)|.

Default example: 10 kΩ · 1 µF → fc ≈ 15.915 Hz (−3.01 dB at fc).

Supported and not supported

Supported

  • Solve any two of R, C, fc
  • τ = RC and ωc = 2πfc
  • Optional magnitude H_lin / H_dB at frequency f
  • API via electrical.lpf

Not supported

  • Higher-order, RLC, or active filters
  • Phase response plots / SPICE export
  • High-pass topology as a separate mode (same corner math; use R/C swap carefully)

Agent / API notes

Capability id: electrical.lpf · tool id: lpf · aliases low-pass-filter · pin calculation_version: 1.0.0.

Stable error codes: NEEDS_TWO_INPUTS, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE.

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Frequently asked questions

Key distinctions behind the calculation.

What is a first-order LPF cutoff?

fc = 1/(2πRC) is the −3 dB corner of an ideal series-R / shunt-C low-pass. Below fc the passband is nearly flat; above fc magnitude falls ≈ −20 dB/decade.

How is this different from the RC time constant tool?

RC time constant focuses on τ and timing multiples. This LPF tool focuses on fc and optional |H(f)| for filter design.

What if I only enter one of R/C/fc?

The API returns NEEDS_TWO_INPUTS — provide any two.

Are active / Sallen–Key filters supported?

Not in v1. Only passive first-order RC.