Resistor Calculator
Decode resistor color bands to find resistance value and tolerance.
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About
Resistor Calculator
Four calculators sit above this. The first reads a resistor's value from its color bands and draws the part as you pick each color. The second and third total a group of resistors wired in parallel or in series. The fourth works out the resistance of a length of wire from its size and the metal it is made of.
How the resistor color code works
Resistors are too small to print numbers on, so the value is painted around the body in colored bands. The scheme is an international standard, IEC 60062, and the same colors carry different meanings depending on which position the band is in.
A four band resistor is the common case. The first two bands are significant figures, the third is a power of ten to multiply them by, and the fourth is the tolerance.
Take the green, red, blue and gold resistor drawn above. Green is 5 and red is 2, so the significant figures give 52. Blue as a multiplier is one million, so the value is 52,000,000 ohms, written 52 MΩ. The gold band is a tolerance of ±5%, which means the real part measures somewhere between 49.4 MΩ and 54.6 MΩ.
The color table
| Color | Significant figures | Multiplier | Tolerance | Temp. coefficient |
|---|---|---|---|---|
| Black | 0 | x 1 | 250 ppm/K (U) | |
| Brown | 1 | x 10 | ±1% (F) | 100 ppm/K (S) |
| Red | 2 | x 100 | ±2% (G) | 50 ppm/K (R) |
| Orange | 3 | x 1K | ±0.05% (W) | 15 ppm/K (P) |
| Yellow | 4 | x 10K | ±0.02% (P) | 25 ppm/K (Q) |
| Green | 5 | x 100K | ±0.5% (D) | 20 ppm/K (Z) |
| Blue | 6 | x 1M | ±0.25% (C) | 10 ppm/K (Z) |
| Violet | 7 | x 10M | ±0.1% (B) | 5 ppm/K (M) |
| Grey | 8 | x 100M | ±0.01% (L) | 1 ppm/K (K) |
| White | 9 | x 1G | ||
| Gold | x 0.1 | ±5% (J) | ||
| Silver | x 0.01 | ±10% (K) | ||
| None | ±20% (M) |
Two of these entries only ever appear in one position. Gold and silver have no significant figure, so a gold band at the left end tells you immediately that you are holding the resistor backwards.
Reading the resistor the right way round
A resistor has no arrow on it, and reading it from the wrong end gives a completely different answer. Brown, black, red is 1 kΩ, and the same part read backwards is red, black, brown, or 200 Ω.
Three things tell you which end is first. There is usually a wider gap between the last two bands than between the others, and the lone band after that gap is the tolerance. The tolerance band is very often gold or silver, and neither of those can be a significant figure. And the first band normally sits closer to its end of the body than the last band does to the other.
When none of that helps, read it both ways and keep the answer that is a standard value. 4.7 kΩ is a part you can buy; 7.4 kΩ is not.
Three, five and six band resistors
Not every resistor has four bands. A three band resistor drops the tolerance band, which by convention means ±20%. Five band resistors add a third significant figure, which is how precision parts get values like 4.99 kΩ that a two figure code cannot express, and this pushes the multiplier and tolerance into the fourth and fifth positions.
A sixth band is either a temperature coefficient in parts per million per kelvin, or on some military parts a reliability rating given as a failure rate per 1000 hours of service. A 50 ppm/K part drifts by 50 millionths of its value for every degree of temperature change, so a 100 kΩ resistor moves about 5 Ω over a 1 degree swing and 150 Ω over a 30 degree one. That matters in a precision reference and does not matter at all in a pull-up.
Preferred values, and why 4.7 exists
Resistors are not made in every value. They come in geometric series chosen so that the tolerance bands of neighbouring values just meet, which is why the numbers look arbitrary until you see the reason. The E12 series, used for ±10% parts, runs:
10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82
Each value is roughly 1.21 times the one before, and every value in between is covered by somebody's tolerance range. E24 doubles the count for ±5% parts, and E96 is used for 1% parts. If your calculated answer is not in the series, either you misread a band or you are looking at a precision part with more figures than you counted.
Resistors in parallel
Wire resistors side by side and the current splits between them, so the combination resists less than any single branch does. The total is the reciprocal of the sum of the reciprocals.
Two useful shortcuts fall out of that. Two equal resistors in parallel give half the value, and n equal resistors give R divided by n. Where the values differ a lot, the smallest one dominates: 10 Ω in parallel with 1 kΩ is 9.9 Ω, so the large resistor barely registers.
This is also the sanity check on your answer. If a parallel total comes out larger than the smallest resistor in the group, something has gone wrong in the arithmetic.
Resistors in series
Wire them end to end and the same current passes through each in turn, so the resistances add.
Series is how you make a value you do not have in the drawer, and how a voltage divider works: the supply voltage splits between the resistors in the same proportion as their resistances, so two equal resistors give half the supply at the join.
Most real circuits are neither purely one nor the other. Work from the inside out, collapsing each parallel group into a single value, then adding the series chain those values sit in.
Resistance of a conductor
Wire has resistance too, and over a long run it stops being negligible. It depends on three things: how long the conductor is, how thick it is, and what it is made of.
The resistance is the length divided by the cross-sectional area times the conductivity. Doubling the length doubles the resistance. Doubling the diameter cuts it to a quarter, because area goes with the square of the radius.
| Material | Conductivity (S/m) | Resistivity (Ω·m) |
|---|---|---|
| Silver | 63,000,000 | 1.587 x 10-8 |
| Copper | 59,600,000 | 1.678 x 10-8 |
| Annealed copper | 58,000,000 | 1.724 x 10-8 |
| Gold | 41,000,000 | 2.439 x 10-8 |
| Aluminium | 35,000,000 | 2.857 x 10-8 |
Silver conducts best and is priced accordingly, which is why copper does almost all of the real work. Aluminium carries about 60% of copper's conductivity for roughly a third of the weight, which is why overhead transmission lines are aluminium and household wiring is not.
A worked case: 100 metres of 0.5 mm diameter copper has a cross-section of 0.196 mm² and comes out at about 8.55 Ω. On a 12 volt circuit drawing 1 amp that wire alone would drop 8.55 volts, which is the whole reason cable sizing tables exist.
Two limits worth knowing. These figures are for direct current; at high frequencies the skin effect pushes current toward the outside of the conductor and the effective resistance rises. And conductivity itself changes with temperature, by roughly 0.4% per degree for copper, so a hot cable resists more than a cold one.
Reading your result
For the color code, check the tolerance before you trust the headline. A ±5% part reading 12 MΩ is anywhere from 11.4 to 12.6 MΩ, and a meter that disagrees with the bands by less than that is not telling you the resistor is wrong.
For the network calculators, enter values in one consistent unit. The calculators do not care whether you mean ohms or kilohms as long as every entry uses the same one, and the answer comes back in that unit.
To go from resistance to current or voltage, use the Ohms Law Calculator, and for the power a resistor has to dissipate before it is chosen, the Voltage Drop Calculator covers the cable side of the same question.
Common questions
Frequently asked questions
The first two bands are digits, the third multiplies them by a power of ten, and the fourth is the tolerance. Green, red, blue, gold reads 5 and 2, times one million, so 52 M ohms at plus or minus 5%.
Start at the end where the bands are grouped closest together. There is a wider gap before the tolerance band, and that band is usually gold or silver, neither of which can be a digit. Reading brown, black, red backwards turns 1 k ohm into 200 ohms.
No tolerance band means plus or minus 20%. Three band resistors are older and rare now, since even cheap modern parts are made to 5%.
A fifth band on a precision resistor is a third significant figure, which lets a part be marked 4.99 k ohms rather than rounded to 5. A sixth band is the temperature coefficient in ppm per kelvin, or on some military parts a failure rate per 1000 hours.
Add the reciprocals of each resistance and take the reciprocal of that sum. Two equal resistors in parallel give half the value, and the total is always smaller than the smallest branch.
Add them. The same current flows through each one, so 10 plus 22 plus 47 ohms in series is 79 ohms. Voltage divides between them in proportion to their resistance.
Resistors are made in preferred series such as E12 and E24, where each step is a fixed ratio rather than a round increment. That is why 4.7 k ohms and 2.2 k ohms are stock values and 5 k ohms generally is not.
Divide the length by the cross-sectional area multiplied by the conductivity of the metal. A 100 metre run of 0.5 mm copper is about 8.55 ohms, which is enough to matter on a low voltage circuit.