Resistance Calculator

Resistance (R) measured in ohms (Ω) is the opposition to current flow in a circuit. When resistors are connected in series, their resistances simply add together. In parallel, the equivalent resistance is always less than the smallest individual resistor — the reciprocal of the total equals the sum of reciprocals (1/Rt = 1/R1 + 1/R2 + ...). Resistor values are marked using color-coded bands: 4-band resistors have 2 value digits + multiplier + tolerance; 5-band resistors have 3 value digits + multiplier + tolerance. Knowing how to read these codes instantly lets you identify components without a multimeter.

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Resistors

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Total Resistance (Series)

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Conductance

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Resistors

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lightbulb Tips

  • •Series: R_total = R1 + R2 + ... (always increases)
  • •Parallel: always less than the smallest resistor
  • •Two in parallel shortcut: Rt = (R1×R2)/(R1+R2)
  • •Gold band = ±5% tolerance, Silver = ±10%

How to Use This Calculator

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Choose a Calculation Mode

Select Series to add resistors in sequence, Parallel for multiple current paths, Color Code to decode resistor bands, or Ohm's Law to find R from voltage and current.

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Enter Resistor Values

For Series or Parallel mode, type in each resistor value in ohms (Ω). You can add up to 10 resistors. For Color Code mode, select the color of each band on the resistor body.

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Calculate Total Resistance

Click Calculate to see the total equivalent resistance and conductance instantly. For parallel circuits, note the result is always lower than the smallest individual resistor.

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Apply the Result

Use the calculated resistance value in circuit design to size current-limiting resistors, verify component values, or confirm Ohm's Law for your circuit's voltage and current.

The Formula

Series resistors increase total resistance because current must flow through each one sequentially. Parallel resistors decrease total resistance because current has multiple paths — like adding more lanes to a road. For two resistors in parallel, a shortcut is Rt = (R1 × R2) / (R1 + R2), called the 'product over sum' formula. For n equal resistors in parallel, Rt = R/n.

Series: Rt = R1 + R2 + ... + Rn | Parallel: 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn

lightbulb Variables Explained

  • Rt Total equivalent resistance in ohms (Ω)
  • R1...Rn Individual resistor values in ohms (Ω)
  • R = V/I Ohm's Law: resistance equals voltage divided by current
  • Color bands Each color represents a digit: Black=0, Brown=1, Red=2, Orange=3, Yellow=4, Green=5, Blue=6, Violet=7, Grey=8, White=9

tips_and_updates Pro Tips

1

For two resistors in parallel, use the product/sum shortcut: Rt = (R1 × R2) / (R1 + R2).

2

n identical resistors in parallel gives Rt = R/n — e.g., four 100Ω resistors in parallel = 25Ω.

3

Resistor tolerance matters: a 100Ω ±5% resistor could measure anywhere from 95Ω to 105Ω.

4

When measuring resistor color codes, hold the tolerance band (gold/silver) on the right and read left to right.

5

E24 series gives 24 standard resistor values per decade (e.g., 10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30...).

Electrical Resistance Calculations for Circuit Design

Electrical resistance is a fundamental property that determines how much a material opposes the flow of electric current, measured in ohms. Whether you are designing circuits, sizing conductors, troubleshooting electrical systems, or studying for an engineering exam, understanding how to calculate resistance in series and parallel configurations is essential. Series resistors simply add their values — three 100-ohm resistors in series yield 300 ohms. Parallel resistors follow the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3, producing a total resistance lower than any individual resistor. Our resistance calculator handles both configurations instantly, supporting up to 10 resistors and showing the step-by-step calculation. It also computes equivalent resistance for mixed series-parallel networks, calculates current and voltage drops across each resistor using Ohm's law, and determines power dissipation — critical for selecting resistors with adequate wattage ratings to prevent overheating and component failure.

Series vs parallel resistance fundamentals

In a series circuit, current flows through each resistor sequentially, and the total resistance is the sum of all individual values: R_total = R1 + R2 + R3. The same current flows through each resistor, but voltage divides proportionally — a 100-ohm and 200-ohm resistor in series with 12V will have 4V across the first and 8V across the second. In parallel circuits, voltage is the same across all resistors, but current divides. Two identical 100-ohm resistors in parallel yield 50 ohms — always less than the smallest individual resistor. The parallel formula 1/R_total = 1/R1 + 1/R2 can be simplified for two resistors: R_total = (R1 × R2) / (R1 + R2).

Practical applications and resistor selection

Resistors serve many purposes beyond simple current limiting. Voltage dividers use two resistors to create a specific voltage from a higher supply — essential in sensor circuits and microcontroller interfaces. Pull-up and pull-down resistors (typically 4.7kΩ to 10kΩ) ensure digital pins read defined states. Current-sensing resistors (0.01Ω to 1Ω) measure current by monitoring voltage drop. When selecting resistors, consider tolerance (1% for precision, 5% for general use), power rating (1/4W for signal circuits, 1W+ for power applications), and temperature coefficient. Standard E24 series values (10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30...) cover most needs within 5% tolerance.

Calculating power dissipation and thermal limits

Every resistor converts electrical energy to heat, and exceeding power ratings causes failure. Power dissipation equals P = I²R = V²/R = V×I. A 100-ohm resistor carrying 100mA dissipates P = 0.1² × 100 = 1 watt — exceeding a standard 1/4W resistor's rating by 4x. Always derate by 50% for reliability: use a 2W resistor for 1W dissipation. In enclosed spaces without airflow, derate further. For high-power applications, consider wirewound resistors (up to 300W), cement resistors, or heatsink-mounted power resistors. Surface-mount resistors (0402, 0603, 0805 packages) handle 1/16W to 1/4W — check datasheets carefully as power handling depends on pad area and PCB copper spreading.

Frequently Asked Questions

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resistance calculator resistor calculator ohm calculator electrical resistance calculator resistance in circuit calculator resistors in series calculator resistors in parallel calculator series parallel resistance calculator
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All formulas verified against official standards.

IEC 60062 — Resistor Marking Codes open_in_new Ohm's Law — Wikipedia open_in_new