RC Time Delay Calculator

This update features additional insights from the original published version.

Voltage dividers are one of the simplest and most widely used circuits in electronics. Their behavior can be extended by adding a capacitor, introducing a time-dependent response. This allows controlled startup delays and ensures that downstream circuits receive power only after the capacitor reaches a required voltage level.

The RC Time Delay Calculator computes key timing results the moment you change any input – no button press needed. A Basic/Advanced toggle at the top of the calculator controls the level of detail. Basic mode shows only the essential fields for quick lookups. Advanced mode unlocks component locking, E-series snapping, target solving, error analysis, and a Bode plot.

The RC Time Calculator uses the following parameters to determine key timing characteristics:

• Input Voltage (Vin) — Supply voltage applied to the top of the resistor divider.
• Resistor R1 — Top resistor. Each resistor has its own unit selector (ohms, kOhm, MOhm). In Advanced mode a Lock toggle keeps the value fixed; when unlocked, the solver can adjust it. An E-series selector (E12, E24, E48, E96, E192, Exact) snaps the value to the nearest standard preferred part number.
• Resistor R2 — Bottom resistor. Same unit, Lock, and E-series controls as R1.
• Output Voltage (Vout) — (Advanced mode) the steady-state voltage the capacitor charges toward, computed from the resistor divider ratio: Vout = Vin × R2 / (R1 + R2). This field is read-only by default. Lock it to set a target output voltage; the solver will then adjust the unlocked resistors to match.
• Steady-State Current — (Advanced mode, read-only) the DC current through the divider once the capacitor is fully charged: I = Vin / (R1 + R2). Auto-scales between nA, μA, mA, and A.
• Capacitance — Capacitor value. Units range from pF to F with automatic display scaling. Same Lock and E-series controls as the resistors.
• Threshold Voltage (Vth) — The voltage the capacitor must reach before the downstream device activates (e.g., the EN pin of a DC-DC converter). Fixed input.
• Time to Threshold — How long it takes the capacitor to charge from 0 V to Vth. Computed automatically. In Advanced mode it can be locked to a target; the solver then selects component values to hit that delay.
• Time to 99% of Output Voltage — Read-only output. Shows how long full charging takes (99% of Vout).

Calculate Time Constant

The capacitor in the circuit follows an exponential charging equation:

V(t) = Vout * (1 – e^(-t / τ))

where Vout is the Output Voltage shown in the calculator (the steady-state voltage the capacitor charges toward), τ (tau) is the time constant, and t is the elapsed time.

The voltage divider defines the maximum voltage the capacitor will reach:

Vout = Vin × (R2 / (R1 + R2))

The time constant τ determines the speed of how the capacitor charges and is calculated as: τ = (R1 × R2) / (R1 + R2) × C

This equation represents the Thevenin equivalent resistance seen by the capacitor, multiplied by its capacitance.

The resulting time constant is: τ = R_th × C

A higher τ value means a slower charge time.

The Time to 99% of Output Voltage output shows how long it takes to reach 99% of Vout. Solving the exponential equation for 99% gives:

t_99 = −τ × ln(1 − 0.99) ≈ 4.605 × τ

The Time to Threshold result shows how long it takes the capacitor to reach Vth: t_threshold = −τ × ln(1 − Vth / Vout)

This is the startup delay before the controlled circuit (such as a DC-DC converter or logic input) becomes active. The result appears in the Time to Threshold field in the calculator.

A higher τ (larger resistors or capacitor) increases both t_threshold and t_99.

Steady-State Current

Once the capacitor is fully charged, it stops drawing current. The DC current through the divider at that point is:
I_steady = Vin / (R1 + R2)

This value appears in the Steady-State Current row (Advanced mode) and is useful for estimating quiescent power draw of the divider network.

Basic/Advanced Mode and Component Solver

The Basic/Advanced toggle is located directly below the share row. Basic mode shows only the essential inputs and outputs. Switching to Advanced reveals the Lock, Series, Computed, and Status columns in the input grid, as well as Output Voltage (Vout), Steady-State Current, error analysis, and the Bode plot.

When a component’s Lock toggle is on (default), its value is fixed. Turning Lock off makes the component solver-controlled: it snaps to the nearest value in the selected E-series on every update, and the Status column shows “Solved (E24)” or similar.

Locking the Time to Threshold field and unlocking one or more components activates the target solver. The solver searches nearby E-series candidates to find the combination that best meets the locked timing target. Locking Output Voltage (Vout) while at least one resistor is unlocked lets the solver pick resistor values that hit a desired output voltage.

When only Capacitance is unlocked against a time target, the solver works analytically: C = τ_needed / R_th, then snapped to the nearest E-series value. When resistors are also unlocked, a bounded neighborhood search evaluates up to 25 000 candidate combinations per update.

If the number of locked targets exceeds the number of unlocked components, or vice versa, the status banner explains the conflict and suggests a fix.

Error Analysis

Real components have manufacturing tolerances, so the actual delay in a production circuit will differ from the nominal value. The optional Enable Error Analysis checkbox (Advanced mode) quantifies how much the outputs can vary.

When enabled, each component row in the input grid shows a tolerance percentage field. Defaults are 1% for R1 and R2, 10% for Capacitance, and 5% for Threshold Voltage (Vth). Two analysis methods run simultaneously:

Worst-case: all eight corners of the tolerance box (R1±, R2±, C±) are evaluated with both extremes of Vth±. The minimum and maximum of Vout, Time to Threshold, and Time to 99% are reported. An orange band on the charge curve shows the full worst-case envelope. If the Vth tolerance range overlaps the achievable Vout range, the worst-case maximum Time to Threshold is reported as unbounded.

Typical (Monte Carlo): 500 samples are drawn with uniform random variation within each tolerance band. The P5 and P95 percentile values are reported. A green band on the charge curve shows the P5–P95 spread. The random generator uses a deterministic seed so repeated evaluations with the same inputs always produce the same results.

Use the Graph range bands dropdown to show worst-case only, typical only, both, or none on the charge curve.

Frequency Response (Bode Plot)

Checking the Frequency Response (Bode Plot) checkbox below the charge curve displays a second plot showing magnitude (dB) and phase (°) versus frequency. This is useful when the RC divider is used as a low-pass filter.

The frequency axis starts at 0 Hz. A 0 Hz signal is also called DC. DC means a steady input voltage that does not change over time, like a battery voltage. At DC, the capacitor has enough time to fully charge and then stops conducting current, so it does not affect the divider. In this condition, the circuit behaves like a plain resistor divider, and the output is set only by R1 and R2.

The DC, or low-frequency, divider ratio is: |Vout/Vin|(0) = R2 / (R1 + R2)

At higher frequencies, the capacitor starts to affect the output. The transfer function magnitude is:

|Vout/Vin|(f) = (R2 / (R1 + R2)) / √(1 + (2π × f × R_th × C)^2)

The cutoff frequency fc is the frequency where the magnitude becomes 3 dB lower than the DC divider value. This does not mean 3 dB below 0 dB. It means 3 dB below the low-frequency value set by R1 and R2.

fc = 1 / (2π × R_th × C) = 1 / (2π × τ)

The phase of Vout relative to Vin is:

φ(f) = −arctan(2π × f × R_th × C)

At DC, the phase is 0°, meaning the output follows the input without phase shift. At high frequency, the phase approaches −90°. The plot marks fc and the corresponding −3 dB point on the magnitude curve.

Share Link

To share your setup, enter a project name in the Project Name field and click Copy shareable link. The link restores all field values exactly as entered.

Summary

The RC Time Delay Calculator models the charging behavior of a capacitor in a voltage divider. Given Vin, R1, R2, Capacitance, and Threshold Voltage (Vth), it computes Output Voltage (Vout), Time to Threshold, and Time to 99% of Output Voltage — all updated automatically as you type. Advanced mode adds a component solver (select E-series values to hit a target delay or output voltage), error analysis (worst-case corner analysis and Monte Carlo P5–P95), a Bode plot, and a shareable link. The calculator is well suited for startup delay design, power-sequencing timing, and enable-pin activation.