Calculator Inputs
Formula Used
For ideal resistors in parallel, the equivalent resistance is found from reciprocal addition: 1 / Req = 1 / R1 + 1 / R2 + ... + 1 / Rn. In AC work, real resistors also have small stray capacitance and lead inductance. This calculator models each branch as R parallel with C, then adds series L.
Zbranch = 1 / (1 / R + j2πfC) + j2πfL. The total impedance is Zeq = 1 / Σ(1 / Zbranch). Current is I = V / Z for voltage input. Voltage is V = I × Z for current input. Power in each resistor is VR2 / R.
How to Use This Calculator
- Enter the operating frequency and select the correct unit.
- Choose whether the source is a known RMS voltage or current.
- Add each resistor value in the selected resistor unit.
- Enter optional capacitance in pF and inductance in nH.
- Add tolerance, TCR, and temperature values when needed.
- Press Calculate to view resistance, impedance, phase, current, and power.
- Use CSV or PDF buttons to save the result.
Parallel Resistance and Frequency Behavior
Parallel resistors look simple at direct current. Each branch shares the same voltage. The total conductance is the sum of each branch conductance. Because of that, the final resistance is always lower than the smallest active branch. This rule is exact for ideal resistors. It is also useful for quick checks before building a circuit.
Why Frequency Changes the View
Real parts are not perfect. A resistor body can have tiny capacitance across its terminals. Leads and tracks can add small inductance. At low frequency, these effects may be invisible. At high frequency, they can change impedance, phase, branch current, and heating. This matters in filters, audio networks, sensors, timing circuits, RF pads, and test fixtures.
Ideal Equivalent Resistance
The ideal result uses reciprocal addition. Add one divided by each resistor. Then invert the sum. This gives the DC equivalent resistance. When two equal resistors are used, the answer is half of one resistor. When many unequal resistors are used, the lowest value branch usually dominates the result.
AC Impedance Model
This tool adds frequency options. Each branch can include a capacitance value in picofarads and an inductance value in nanohenries. The calculator treats the resistor and capacitance as parallel. It then places the lead inductance in series with that branch. This creates a complex impedance, with real and imaginary parts.
Phase and Power
The impedance angle shows phase shift. A positive angle suggests inductive behavior. A negative angle suggests capacitive behavior. A near zero angle means the network is mostly resistive. RMS current is found from the selected source. Real power is calculated in the resistor part, not in the ideal reactive part.
Tolerance and Temperature
Resistors change with tolerance and temperature. The tolerance setting estimates a possible ideal resistance band. The temperature coefficient changes each nominal value from the reference temperature to the operating temperature. This helps when a design must stay accurate during warm operation, field testing, or enclosure heating.
Reading the Results Safely
Do not judge the network from one number only. Read ideal resistance, complex impedance, magnitude, phase, and power together. A low ideal resistance can still show a different AC magnitude when stray parts are entered. A branch with more capacitance may take extra current at high frequency. A branch with more inductance may limit current or add positive phase. Watch the wattage result for each branch. Use a safety margin when selecting real parts. Check the CSV report when values need documentation or later comparison. This keeps assumptions clear during design reviews and lab checks.
Practical Design Use
Use this calculator to compare DC resistance with AC impedance. If the two values are close, parasitic effects are small at the selected frequency. If phase or magnitude shifts are large, the layout or part style may need review. Keep leads short. Use suitable packages. Confirm critical circuits with measurement.
Example Data Table
| Frequency | R1 | R2 | R3 | C per branch | L per branch | Expected Ideal R |
|---|---|---|---|---|---|---|
| 1 kHz | 100 Ω | 200 Ω | 300 Ω | 0 pF | 0 nH | 54.545 Ω |
| 10 MHz | 1 kΩ | 2 kΩ | 4.7 kΩ | 2 pF | 5 nH | 623.894 Ω |
| 100 MHz | 50 Ω | 75 Ω | 150 Ω | 1 pF | 2 nH | 25 Ω |
FAQs
1. What does this calculator find?
It finds ideal equivalent resistance and frequency-dependent impedance for resistors in parallel. It can also estimate branch current, phase angle, power, tolerance range, temperature shift, RC corner frequency, and LC resonance.
2. Are pure resistors affected by frequency?
Ideal resistors are not affected by frequency. Their resistance stays constant. Real resistors may show small capacitive or inductive effects at high frequency, especially with long leads, large packages, or sensitive RF layouts.
3. Why is equivalent resistance lower than each branch?
Parallel branches create more current paths. Total conductance increases as each branch is added. Since resistance is the inverse of conductance, the equivalent resistance becomes lower than the smallest individual resistor.
4. What does capacitance in pF mean here?
It represents stray capacitance across a resistor branch. This capacitance can pass more current as frequency rises. That changes the branch impedance and may create a capacitive phase shift.
5. What does inductance in nH mean here?
It represents small lead, trace, or package inductance in a branch. Inductive reactance grows with frequency. At high frequency, it can increase impedance and shift the phase toward inductive behavior.
6. What is phase angle?
Phase angle shows the reactive part of the total impedance. Zero degrees means mostly resistive behavior. Positive values suggest inductive behavior. Negative values suggest capacitive behavior.
7. What source value should I enter?
Enter the RMS voltage if your circuit is driven by a known voltage. Enter RMS current if current is fixed. The calculator uses that source to estimate total current, voltage, and branch power.
8. How is power calculated?
Power is calculated in the resistor part of each branch. Ideal capacitance and ideal inductance do not consume real power. The result helps check heating and resistor wattage needs.
9. What does TCR mean?
TCR means temperature coefficient of resistance. It describes resistance change per degree Celsius, usually in ppm per degree. Use it when resistor temperature is far from the reference temperature.
10. Can I leave capacitance and inductance as zero?
Yes. Use zero when you want an ideal parallel resistor calculation. The impedance result will match the ideal resistance, with near zero phase, when all parasitic values are zero.
11. Is this suitable for RF design?
It is useful for estimates and design checks. For final RF work, also consider layout, package data, ground return paths, and measurements from a network analyzer or suitable lab instrument.