CalculatorShelf
Browse calculators
Browse by shelf

Choose a focused collection, or open the complete directory.

All calculators
StoragePlan capacity, performance, and reliability decisions for storage and PC hardware.Home ProjectsEstimate materials and quantities for practical home projects with visible assumptions.Pool & WaterEstimate pool volume from measured dimensions; use the guides to understand product and safety boundaries.ShippingEstimate shipping quantities, costs, and loading geometry before requesting a quote.LifestyleHandle everyday sizing, photography, wrapping, and seasonal planning questions.SportsExplore pace, motion, and sizing calculations with explicit assumptions and limits.BusinessPlan margin and language-service decisions from entered prices, costs, and volumes.Math & EducationCalculate arithmetic, scientific expressions, units, dates, algebra, physics, and education formulas with visible methods.FinanceCompare currency, bills, discounts, and fixed-rate loan scenarios with visible rates, rounding, and assumptions.
All calculatorsMethodology

RC Filter Calculator

Find the cutoff frequency, time constant, gain in dB and phase shift of a first-order RC low-pass or high-pass filter, with a response table around cutoff.

Interactive calculator · Method RC-FILTER-1.0 · Last reviewed: 2026-11-04

Calculate your scenario

Cutoff frequency fc = 1 ÷ (2π R C) and time constant τ = R × C.

Your inputs

Try an example

Default worked example. Edit the inputs to calculate your scenario.

Default worked example

Cutoff frequency (−3 dB) 1.5915 kHz
Time constant τ = RC 100 µs
Gain at test frequency 0.8467 V/V
Gain at test frequency in dB -1.45 dB
Phase shift at test frequency -32.14°

fc = 1 ÷ (2π × 10 kΩ × 10 nF) = 1.5915 kHz; at 1 kHz the low-pass gain is -1.45 dB.

How to use the calculator

Enter the resistance and capacitance with their units, choose low-pass or high-pass, and enter a frequency to see the gain and phase there.

What the result means

A 10 kΩ resistor with a 10 nF capacitor gives a cutoff near 1.5915 kHz; a 1 kHz signal through the low-pass version keeps about 0.8467 of its amplitude (−1.45 dB) and lags by about 32.14°.

Formula and units

Cutoff frequency fc = 1 ÷ (2π R C) and time constant τ = R × C. With x = f ÷ fc, a low-pass gain is 1 ÷ √(1 + x²) with phase −atan(x); a high-pass gain is x ÷ √(1 + x²) with phase +atan(1 ÷ x). Gain in dB = 20 log₁₀(gain).

Worked examples

10 kΩ and 10 nF low-pass at 1 kHz: Resistance: 10 selected unit; Capacitance: 10 selected unit; Test frequency: 1000 Hz; Resistance unit: k; Capacitance unit: n; Filter type: low.
Example result: Cutoff frequency (−3 dB): 1.5915 kHz; Time constant τ = RC: 100 µs; Gain at test frequency: 0.8467 V/V; Gain at test frequency in dB: -1.45 dB; Phase shift at test frequency: -32.14°.

1.6 kΩ and 100 nF high-pass at 100 Hz: Resistance: 1.6 selected unit; Capacitance: 100 selected unit; Test frequency: 100 Hz; Resistance unit: k; Capacitance unit: n; Filter type: high.
Example result: Cutoff frequency (−3 dB): 994.7184 Hz; Time constant τ = RC: 160 µs; Gain at test frequency: 0.1 V/V; Gain at test frequency in dB: -20 dB; Phase shift at test frequency: 84.26°.

Limitations and common mistakes

Ideal first-order model with an ideal voltage source and an unloaded output. Real source resistance, load impedance, capacitor tolerance, ESR and parasitics shift the response. Educational arithmetic only; it does not rate components for voltage, power or tolerance.

Mixing up nF and µF; a factor of 1,000 in capacitance moves the cutoff by the same factor.

Sources and assumptions

Method RC-FILTER-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.