Resistance Calculator

Calculate electrical resistance from resistivity, wire length, cross-section, and temperature coefficient.

Series and Parallel Resistor Networks

BrainyCalculators editorial insight — unique to this tool

Series R_total = R₁+R₂; parallel 1/R = 1/R₁+1/R₂. LED current-limiting resistor from Ohm's law: (5V − 2V) / 0.02A = 150 Ω. 4-band color code identifies values on through-hole parts.

When to use this calculator

Use for combined resistance in circuits. For V=IR voltage, use Voltage.

Solving full circuit V, I, R, and power?

This page focuses on resistance value. For complete Ohm’s law, use the Ohm’s Law Calculator →

What is Electrical Resistance?

Resistance calculators find ohms from wire dimensions and resistivity or solve V/I in a circuit branch. Temperature coefficient adjusts for heat.

Use this page when resistance value or wire sizing is the unknown. Ohm’s law page integrates V, I, R, and P together.

Voltage calculator emphasizes potential difference solves.

Resistance Formulas

Series Circuit

R_total = R₁ + R₂ + … + Rₙ

Total resistance equals the sum of all individual resistors. Current is the same through all.

Parallel Circuit

1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ

Reciprocal of total equals sum of reciprocals. Voltage is the same across all branches.

How to Use the Resistance Calculator

1

Choose Circuit Type

Select Series for resistors connected end-to-end, or Parallel for resistors connected side-by-side.
2

Enter Resistor Values

Start with 3 inputs. Click "+ Add Resistor" to include up to 8 resistors. Values are in Ohms.
3

Remove Unused Inputs

Click the × button next to any row to remove it. A minimum of 2 resistors is required.
4

View Results

Total resistance is shown in Ω, kΩ, and MΩ. Parallel mode also shows conductance in Siemens.

Example: 3 Resistors

Series: 100Ω, 220Ω, 470Ω

R = 100 + 220 + 470

R = 790 Ω = 0.79 kΩ

Parallel: 100Ω, 220Ω, 470Ω

1/R = 1/100 + 1/220 + 1/470

R ≈ 62.3 Ω

How the Resistance Calculator Works

Formula, assumptions, and calculation steps for this engineering tool.

Methodology

Engineering calculators apply standard unit conversions and formula relationships after normalizing measurements to compatible units.

Calculation Steps

Enter dimensions, loads, rates, or electrical values.
Convert the inputs into the formula unit system.
Apply the engineering equation or conversion factor.
Return the result with units and supporting context.

Assumptions and Limits

Material behavior is assumed ideal unless fields specify otherwise.
Code checks, safety factors, and site conditions may require professional review.
Use a qualified engineer for design-critical decisions.

Frequently Asked Questions

What is the difference between series and parallel?

In a series circuit, resistors are connected end-to-end so the same current flows through all of them. The total resistance is the sum. In a parallel circuit, resistors share the same two nodes so the same voltage appears across each. The total resistance is always less than the smallest individual resistor.

When would you use parallel resistors?

Parallel resistors are used to decrease total resistance or to handle higher current/power. They are common in power distribution, current sensing, and load balancing. House wiring uses parallel circuits so each appliance gets the full supply voltage.

What is conductance?

Conductance is the reciprocal of resistance: G = 1/R, measured in Siemens (S). It represents how easily current flows. In parallel circuits the total conductance is simply the sum of individual conductances: G_total = G₁ + G₂ + … + Gₙ.

What are standard resistor values?

Resistors are manufactured in standardized E-series values. The E12 series has 12 values per decade: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 (and multiples/fractions thereof). The E24 series has 24 values, and E96 has 96 values per decade for precision applications.

Why is parallel resistance always less than the smallest resistor?

Adding any parallel path always gives current more routes to flow, increasing total current for the same voltage. By Ohm's Law (R = V/I), higher current means lower equivalent resistance. Even adding a very large resistor in parallel slightly lowers the total below the previous smallest value.

Real-World Applications

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LED Current Limiting Resistor Selection

An LED requires a specific forward current (typically 20 mA) but cannot regulate its own current — without a series resistor it would burn out. Using Ohm's Law: R = (Vsupply − VLED) / ILED. For a 5V supply driving an LED with 2V forward voltage at 20 mA: R = (5 − 2) / 0.02 = 150 Ω. This is one of the most common resistor calculations in electronics prototyping.

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Electrical Cable Sizing & Voltage Drop

Electrical engineers calculate the resistance of cable runs to determine voltage drop at the end of long cable runs — R = ρL/A where ρ is copper resistivity (1.68 × 10⁻⁸ Ω·m), L is cable length, and A is cross-sectional area. Cable is upsized until voltage drop stays within the permitted 3–5% of supply voltage to ensure adequate voltage at load devices.

🌡️

Heating Element Design

Electric heating elements (toasters, hair dryers, electric ovens) are designed using P = V²/R — specifying nichrome wire of appropriate resistivity and dimensions to produce the target wattage at the supply voltage. Increasing resistance reduces power; decreasing resistance increases power output and heat generation.

🎛️

Voltage Divider Circuit Design

A voltage divider uses two series resistors to produce a fraction of the input voltage — Vout = Vin × R2 / (R1 + R2). This fundamental circuit scales sensor signals to ADC input ranges, biases transistor base voltages, and creates reference voltages in analogue circuit design.

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Battery Internal Resistance & Capacity Testing

Battery health is assessed by measuring internal resistance under load — a fresh AA battery has ~0.1 Ω internal resistance; a degraded battery may have > 1 Ω. Using V = IR, the internal resistance causes a voltage drop under load that reduces available terminal voltage — high internal resistance is a reliable indicator of battery age and capacity degradation.

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Biomedical — Electrical Impedance Analysis

Bioelectrical impedance analysis (BIA) devices measure the electrical resistance of body tissues to estimate body composition (lean mass vs. fat). Different tissues have different resistivities — fat tissue has higher resistance than lean muscle tissue because it contains less water and electrolytes. Body fat percentage is inferred from the total impedance measurement.

Common Mistakes

Applying Ohm's Law to non-ohmic components

Ohm's Law (V = IR) assumes resistance is constant regardless of voltage and current — this holds for resistors and most metallic conductors at constant temperature. It does not hold for diodes (resistance varies dramatically with voltage direction and magnitude), transistors, light bulbs (resistance changes with temperature), or electrolytic capacitors. Applying V = IR to these components produces incorrect current estimates.

Using the wrong formula for parallel resistance

The equivalent resistance of resistors in parallel is 1/Rtotal = 1/R1 + 1/R2 + ... — not the sum. For two equal resistors R in parallel, Rtotal = R/2. A common mistake is adding parallel resistances directly (giving R1 + R2) instead of computing the reciprocal of the sum of reciprocals. Only series resistances add directly.

Ignoring temperature coefficient when precision matters

Most resistors have a temperature coefficient — their resistance changes with temperature. Carbon film resistors change by 200–600 ppm/°C; metal film resistors by 50–100 ppm/°C; precision wirewound resistors by 5–10 ppm/°C. In precision measurement circuits and instrumentation, resistance change with temperature must be accounted for to maintain accuracy across the operating temperature range.

Confusing resistance with impedance in AC circuits

In DC circuits, opposition to current flow is purely resistive (R). In AC circuits, capacitors and inductors also oppose current through reactance (X) — and total impedance Z = √(R² + X²) using the Pythagorean relationship. Using DC resistance calculations in AC circuits ignores the frequency-dependent reactance contributions, leading to significant errors in current and power calculations.

Not accounting for contact resistance in precision measurements

In low-resistance measurements (milliohm range), the resistance of connection wires, PCB traces, and connector contacts becomes significant and must be excluded from the measurement. Four-wire (Kelvin) measurement techniques eliminate lead and contact resistance from low-resistance measurements by using separate current-carrying and voltage-sensing connections — a critical technique for precision resistance calibration and battery internal resistance testing.

Common Material Resistivity Quick Reference (at 20°C)

Material	Resistivity (Ω·m)	Common Use
Silver	1.59 × 10⁻⁸	High-frequency PCB traces, RF connectors
Copper	1.68 × 10⁻⁸	Electrical wiring, PCB traces
Aluminium	2.82 × 10⁻⁸	Power lines, structural wiring
Nichrome	1.10 × 10⁻⁶	Heating elements, resistance wire
Silicon (intrinsic)	6.4 × 10²	Semiconductor base material
Glass	10¹⁰ – 10¹⁴	Electrical insulation

References

Ohm, G.S. Die galvanische Kette, mathematisch bearbeitet. Berlin, 1827.
Hayt, W.H. and Kemmerly, J.E. Engineering Circuit Analysis. McGraw-Hill, 2018.
Horowitz, P. and Hill, W. The Art of Electronics. Cambridge University Press, 2015.
Kittel, C. Introduction to Solid State Physics. Wiley, 2004.
NIST. Electrical Resistivity of Common Materials. nist.gov, 2024.