Resistance Calculator

Introduction

This resistance calculator helps you find the resistance of a resistor, a wire, or a whole circuit. Resistance tells you how hard it is for electric current to flow. We measure it in ohms (Ω).

The tool has five parts:

Color Code: Pick the color bands on a resistor and get its value, tolerance, and range. You can also work backward and turn a value into color bands, or decode SMD chip codes.
Parallel: Add up resistors that share the same two points. The total is always smaller than the smallest one.
Series: Add up resistors placed one after another. The total is just the sum.
Conductor / Wire: Enter a wire's length, diameter, and material to get its resistance, area, and AWG size.
Ohm's Law & Power: Fill in any two of voltage, current, resistance, or power, and get the other two.

Every tab shows step-by-step math, so you can see how the answer was found. Charts let you compare values fast. It works for homework, hobby projects, and real wiring jobs.

How to use our Resistance Calculator

Pick a tab, type in what you know about your resistor, wire, or circuit, and the calculator gives you the resistance value, tolerance range, total resistance, conductance, power, and full step-by-step math with charts.

Color Code tab

Number of Bands: Choose 3, 4, 5, or 6 bands to match the stripes printed on your resistor.

1st and 2nd Significant Digit: Click the color chip that matches the first and second stripe on the resistor. These give the main digits of the value.

3rd Significant Digit: Only shows for 5 and 6 band resistors. Pick the color of the third stripe.

Multiplier: Pick the color of the multiplier band. It tells how many zeros to add to the digits.

Tolerance: Pick the color of the tolerance band, like gold for ±5%. Three band resistors skip this and use ±20%.

Temperature Coefficient: Only shows for 6 band resistors. Pick the last band color to get the ppm/°C rating.

Reverse Lookup

Target Resistance: Type the ohm value you want and choose Ω, kΩ, MΩ, or GΩ from the drop-down.

Tolerance: Pick the tolerance you need, such as ±1% or ±5%.

Band Count to Generate: Choose how many bands the resistor should have, then press Generate Color Code to see the band colors.

SMD Code Decoder

SMD Code: Type the code printed on a surface-mount resistor, like 472, 4702, 4R7, or 01C, then press Decode.

Parallel and Series tabs

Resistor Values: Type each resistor value, split by commas, spaces, or new lines.

Unit for All Values: Choose Ω, kΩ, or MΩ. The same unit is used for every value you typed.

Conductor / Wire tab

Conductor Length: Type how long the wire is and pick a unit, such as m, ft, or km.

Conductor Diameter: Type the wire thickness and pick a unit. The wire is treated as solid and round.

Material Preset: Pick a metal like copper or aluminium, or choose Custom to enter your own number. For PCB work, the Trace Width Calculator uses the same idea on copper traces.

Conductivity (σ): This fills in on its own from the preset. Change it if you need a different value, and pick S/m, MS/m, or % IACS.

Resistance Output Unit: Choose how the answer is shown, from µΩ up to MΩ, or leave it on Auto-scale.

Area Output Unit: Choose mm², cm², m², in², or kcmil for the cross-section area.

Ohm's Law & Power tab

Voltage (V): Type the volts and pick a unit, or leave it blank if you want the calculator to find it.

Current (I): Type the amps and pick a unit, or leave it blank.

Resistance (R): Type the ohms and pick a unit, or leave it blank.

Power (P): Type the watts and pick a unit, or leave it blank. Fill in any two of these four boxes and press Calculate to get the other two.

What Is Resistance?

Resistance is how much a material fights the flow of electric current. We measure it in ohms (Ω). A low resistance lets current move easily, like a wide pipe lets water flow. A high resistance slows current down, like a narrow pipe. The opposite of resistance is conductance, measured in siemens (S), and it is just 1 ÷ R.

Ohm's Law and Power

Ohm's Law links three things: voltage (V), current (I), and resistance (R). The rule is V = I × R. If you know any two, you can find the third. Power tells you how much energy the part uses each second, in watts. You can find it with P = V × I, P = I² × R, or P = V² ÷ R. Power turns into heat, so resistors have a watt rating you should not go over.

Resistor Color Codes

Small resistors are too tiny to print numbers on, so makers paint colored bands on them instead. Each color stands for a number. The first bands give the digits, the next band is the multiplier (how many zeros to add), and the band after that is the tolerance, which tells you how far off the real value can be. Gold means ±5% and silver means ±10%. A 6th band, when there is one, shows the temperature coefficient in ppm/°C, which tells you how much the value drifts when the part gets hot.

3 bands: two digits, a multiplier, and an assumed ±20% tolerance.
4 bands: two digits, a multiplier, and a tolerance band.
5 bands: three digits, a multiplier, and a tolerance band (more exact parts).
6 bands: same as 5, plus a temperature coefficient band.

Flat surface-mount (SMD) resistors use printed codes instead of colors. A 3-digit code like 472 means 47 followed by 2 zeros, or 4,700 Ω. An "R" marks a decimal point, so 4R7 is 4.7 Ω. EIA-96 codes use two numbers and a letter for very small, exact parts.

Series and Parallel Resistors

When resistors sit in a line, one after another, they are in series. You just add them up: R = R₁ + R₂ + R₃. The total is always bigger than any single one.

When resistors sit side by side and share the same two points, they are in parallel. Current splits between them, so the total drops. You add the reciprocals: 1/R = 1/R₁ + 1/R₂ + 1/R₃. The total is always smaller than the smallest resistor in the group. In AC circuits, resistance combines with reactance from capacitors and coils, which the Impedance Calculator works out.

Wire and Conductor Resistance

Even plain wire has some resistance. It depends on three things: how long the wire is, how thick it is, and what metal it is made of. The formula is R = ρL ÷ A, where ρ (rho) is the resistivity of the metal, L is the length in meters, and A is the cross-section area in square meters. For a round wire, A = πd² ÷ 4.

Longer wire means more resistance. Thicker wire means less. Silver and copper conduct best, which is why most house and device wiring uses copper. Thin or long wire drops voltage and heats up, so picking the right wire gauge (AWG) matters for safety and for keeping power loss low.

Common Resistance Units

1 kΩ = 1,000 ohms
1 MΩ = 1,000,000 ohms
1 mΩ = 0.001 ohms

Formulas used

Resistor color code value (4-band)

R = (10 d_1 + d_2) \times M

Resistor color code value (5/6-band)

R = (100 d_1 + 10 d_2 + d_3) \times M

Tolerance range

\Delta R = R \cdot \frac{T\%}{100}, \quad R_{min} = R - \Delta R, \quad R_{max} = R + \Delta R

Parallel equivalent resistance

\frac{1}{R_{eq}} = \sum_{i=1}^{n} \frac{1}{R_i}

Series equivalent resistance

R_{eq} = \sum_{i=1}^{n} R_i

Conductor cross-sectional area and resistance

A = \frac{\pi d^2}{4}, \quad R = \frac{L}{\sigma A}, \quad \rho = \frac{1}{\sigma}

Nearest AWG size from diameter (m)

\text{AWG} = 36 - 39 \cdot \frac{\ln\!\left(\frac{d}{0.000127}\right)}{\ln 92}

Ohm's law and power

V = I R, \quad P = V I = I^2 R = \frac{V^2}{R}, \quad G = \frac{1}{R}

Frequently asked questions

Which end of a resistor do I read the color bands from?

Start from the end where the bands are grouped closest together. The tolerance band, often gold or silver, has a wider gap before it and sits at the far end. Read toward that band.

What if I read the bands backward?

You get a very different value. If one end has a gold or silver band, that end goes last. If both ends look the same, check with a multimeter or try both ways in the Color Code tab and see which value matches a common part size.

What does E24 standard value mean in the results?

E24 is a list of 24 common resistor values makers actually sell, like 10, 22, 47, and 68. If your decoded value is on that list, the tool marks it with a check. If not, it shows the closest E24 part you can buy.

Can I mix ohms and kilohms in the parallel or series list?

No. One unit is used for every value you type. Convert them first, or split the job into two runs. For example, type 4700 with the Ω unit instead of 4.7 kΩ.

Why is my parallel total smaller than every resistor I typed?

That is normal. Parallel paths give current more ways to flow, so the circuit fights the current less. The total is always below the smallest resistor in the group.

What does the inconsistent inputs error mean?

It means the numbers you typed do not agree with each other. For example, 12 V with 100 Ω must give 0.12 A. If you typed a different current, clear that box or fix the value.

What does % IACS mean in the conductivity list?

IACS compares a metal to pure annealed copper. 100% IACS equals 58,000,000 S/m. Aluminium is about 61% IACS. Use it if your wire spec sheet lists conductivity that way.

What is kcmil in the area unit list?

Kcmil means thousand circular mils. It is used for large power cables in the United States. One circular mil is the area of a wire that is one thousandth of an inch across.

Why does the reverse lookup say nearest code instead of exact?

Color bands can only show 2 or 3 digits plus a multiplier. Values like 4,733 Ω cannot be painted on a resistor, so the tool picks the closest code it can make and tells you the small difference.

My SMD code was not recognized. What went wrong?

The tool reads 3-digit codes (472), 4-digit codes (4702), R codes (4R7), and EIA-96 codes (01C). Codes with extra letters, a bar over them, or a maker's date code will not decode. Type only the resistance part.

What does a 0 ohm resistor look like?

It has one single black band. It is a jumper wire, not a real resistor, and it is used to link two spots on a circuit board. The color tool needs at least three bands, so you do not need to decode it.

What does energy in 1 hour mean on the Ohm's Law tab?

It shows how much energy the part uses if it runs for one full hour, in joules and watt-hours. A 10 W load uses 10 Wh in an hour. This helps you guess running cost.

Does this work for AC circuits?

It handles the resistance part only. AC circuits with capacitors or coils also have reactance, which changes with frequency. For those, you need impedance instead of plain resistance.

Why does my multimeter read a bit different from the calculated value?

Two reasons. Real parts vary within their tolerance band, and your meter leads add a small amount of resistance. Check that the reading falls inside the min and max range shown.

What is the temperature coefficient band good for?

It tells how much the value drifts when the part heats up, in parts per million per degree. A 100 ppm/°C resistor changes about 0.01% per degree. Low numbers matter for meters and sensors.

Rate this calculator