Resistor Calculator

Resistor Color Code

Most through-hole resistors are too small to print a value on, so they carry colored bands instead. The system, standardized internationally as IEC 60062, assigns a digit to each of ten colors from black (0) to white (9). A mnemonic many students learn is the order of the rainbow between black-brown and grey-white: red, orange, yellow, green, blue, violet.

Read the bands starting from the end with the bands grouped closest together; the tolerance band is usually set slightly apart and is often gold or silver. On a four-band resistor the first two bands are significant digits, the third is the multiplier (the power of ten), and the fourth is the tolerance. Green, red, blue, gold, the default above, reads 5 and 2, times 10⁶, giving 52 MΩ with a tolerance of ±5%, so the actual value may lie anywhere from 49.4 to 54.6 MΩ.

Five-band resistors, common for precision parts with tolerances of 1% or better, have three significant digits before the multiplier. Six-band resistors add a final band for the temperature coefficient, the amount the resistance changes per kelvin of temperature change, in parts per million. Three-band resistors have only two digits and a multiplier and imply a tolerance of ±20%. Gold and silver in the multiplier position divide by 10 and 100, so red, violet, gold reads 2.7 Ω.

Resistors are made in preferred values from the E-series, such as E12 (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82) for 10% parts and E24 or E96 for tighter tolerances. Knowing the series helps check a reading: a band combination that does not match a standard value often means the resistor has been read from the wrong end. When in doubt, measure it with a multimeter, especially on older or heat-discolored parts.

Surface-mount resistors use printed numeric codes instead: three or four digits where the last digit is the number of zeros (103 = 10 kΩ), or the EIA-96 code of two digits and a letter for 1% parts.

Resistors in parallel:

Resistors are in parallel when each one connects across the same two points, so they all share the same voltage and the current divides among them. Each extra path lets more current flow, so the total resistance is always lower than the smallest individual resistor. Add the reciprocals of the resistances and take the reciprocal of the sum. For the default list of 10, 2, 38, 23, 38, 23 and 21 Ω, the result is about 1.27 Ω, below the 2 Ω resistor alone.

1/R_total = 1/R₁ + 1/R₂ + … + 1/Rₙ

For two resistors this simplifies to R = R₁ × R₂ ÷ (R₁ + R₂).

Resistors in series:

Resistors are in series when they are connected end to end, so the same current passes through each in turn and the voltage divides among them. The total resistance is simply the sum, R = R₁ + R₂ + … + Rₙ, so the default list adds up to 155 Ω. Series resistors are used to build voltage dividers and to reach values that are not available as a single part.

Resistance of a conductor:

The resistance of a uniform wire grows with its length and shrinks with its cross-sectional area: R = L ÷ (σ × A) = ρ × L ÷ A, where σ is the conductivity and ρ = 1/σ the resistivity of the material. For a round wire, A = π × d² ÷ 4. One hundred feet of copper wire 0.05 inch across, close to 16 AWG, has a resistance of about 0.40 Ω.

Conductivity depends on temperature, so tables quote it at 20 °C; metals conduct less well as they warm. The values used by the calculator are listed below.

Frequently asked questions