// multi-utility computation suite · offline · instant · precise
┌──────────────────────────┐
│ [c] calcalyst_ │
│ computation suite │
└──────────────────────────┘
// select a module to initialize
/ search↵ open firstesc close
// adsenseEMPTY_LEADER_SLOT728×90
// keyboard shortcuts
/focus search
Escclear search · close calc
Enteropen first result
↑↓navigate list
?toggle this panel
// adsenseMOBILE_ANCHOR_SLOT320×50
// keyboard_shortcuts
/focus search
↑↓navigate module list
Enter
open first result from search
open highlighted
compute when module is open
compute when focused in a field
Escclose module · clear selection
⌫
sci.Laplace-transform-RC-circuit Calculator
Calculates the RC circuit step response V_out(t) = V_in(1 − e^(−t/RC)) using Laplace transforms and derives the −3 dB cutoff frequency f_c = 1/(2πRC). An RC filter with R = 10 kΩ and C = 10 nF has f_c = 1,592 Hz — commonly used for audio tone shaping and ADC anti-aliasing.
Inputs
R Ohm
Opposition to current flow (Ω). V = IR. Resistors in series add; in parallel their reciprocals add.
C F
Ability to store electric charge (F). Capacitors charge quickly and release energy fast. Common values: pF to μF.
V0 V
Electric potential difference (V). Drives current through a circuit. Household: 120 V (US) or 230 V (EU/UK).
T Ms
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Results
voltage at time t (V)
Electric potential difference between the two terminals (V). In AC systems, quoted as RMS — 230 V mains has a peak of ~325 V.
time constant τ = RC (μs)
Time for the capacitor (or inductor) to reach 63.2% of its final value. τ = RC. After 5 time constants (~99.3%), the circuit is effectively at steady state.
-3dB cutoff frequency (kHz)
Frequency at which output power drops to half (−3 dB). For a low-pass filter: signals below this pass; above this are attenuated. For RC circuits: Fc = 1/(2πRC).
energy stored in capacitor (μJ)
Sample size or count used in the calculation.
V(t) = V₀·e^(-t/τ)
Reference formula or conversion factor shown for context.