How this instrument works
Four painted bands turn into one number: two significant digits, a multiplier that sets how many places those digits shift, and a tolerance that bounds how far the finished part can drift from that nominal figure. The formula reads the first two bands as a two-digit number — R = (10·d₁ + d₂) × multiplier — then the fourth band states a percentage either side of that result. The scheme was standardized by the Radio Manufacturers Association in the 1920s and later folded into IEC 60062, so the same eleven colors decode identically on parts made in Shenzhen or Sheffield.
The digit colors are not arbitrary. Red, orange, yellow, green, blue and violet — bands 2 through 7 — run in the same order as the visible spectrum from long wavelength to short, which is why the sequence feels learnable rather than random after the first few resistors. Black and brown, the two darkest colors, were given to the lowest digits, 0 and 1, and grey and white, which have no single spectral wavelength, were appended at the top end for 8 and 9. The same eleven colors then do double duty: gold and silver mean ×0.1 and ×0.01 when they sit in the multiplier position, but ±5% and ±10% when they sit in the tolerance position.
The code states a nominal value and a manufacturing tolerance, and nothing beyond that. It says nothing about power rating, voltage rating or temperature coefficient, and it cannot describe a part that has already drifted from age, heat or mechanical stress — only a multimeter reading confirms what a specific resistor measures right now. It also assumes exactly four bands; five- and six-band resistors carry a third significant digit and sometimes a temperature-coefficient band, and reading one of those as though it were four bands misplaces the decimal point by a factor of ten.
- Pick the color of Band 1 (first digit) and Band 2 (second digit) — these set the resistor's two significant figures, read in the direction away from the tolerance band.
- Choose Band 3 (multiplier), the color that tells the instrument how many zeros — or, for gold and silver, what fraction — to apply to those two digits.
- Set Band 4 (tolerance) to the color of the widest-spaced final band, which states how far the true resistance may sit from the nominal figure.
- Read Resistance for the nominal value in ohms, kilohms or megohms, then check Minimum and Maximum for the true range a multimeter should find.
Worked example — yellow, violet, red, gold
Read the four bands left to right: yellow, violet, red, gold. Yellow sets Band 1 (first digit) to 4 and violet sets Band 2 (second digit) to 7, so the two significant digits read 47. Red as Band 3 (multiplier) means ×100, so the formula gives R = (10 × 4 + 7) × 100 = 47 × 100 = 4700 Ω — a value so common that '4k7' has become its own shorthand on parts lists.
Gold as Band 4 (tolerance) states ±5%, so Minimum reads 4700 × (1 − 0.05) = 4465 Ω and Maximum reads 4700 × (1 + 0.05) = 4935 Ω. A bench meter showing 4522 Ω on this part is not a defect — it sits inside that printed range — while a reading of 4300 Ω would mean either a miscounted band or a resistor that has drifted out of spec.
Questions
Why does the digit sequence run black, brown, red, orange, yellow, green, blue, violet, grey, white?
Because bands 2 through 7 — red, orange, yellow, green, blue, violet — follow the same order as the visible spectrum from long wavelength to short, giving six colors an instantly learnable sequence. Black and brown, the darkest colors, were assigned to the lowest digits, 0 and 1; grey and white, which have no single wavelength, were added at the top for 8 and 9. The scheme dates to the Radio Manufacturers Association's 1920s color code, later folded into IEC 60062.
Why does gold mean two different things depending on which band it's in?
Because the color code reuses its eleven colors across two different jobs. In Band 3 (multiplier), gold means ×0.1 and silver means ×0.01 — the only two multiplier colors below one. In Band 4 (tolerance), that same gold means ±5% and silver means ±10%. Position, not color alone, decides which meaning applies, which is why the bands are always read from the tightly grouped digit end toward the isolated tolerance band.
Does the color code guarantee the resistor measures exactly that value?
No — it states a nominal value and a tolerance, nothing more. A 4,700 Ω part with a gold band promises only that its true resistance sat somewhere between 4,465 Ω and 4,935 Ω when manufactured; heat, age and mechanical stress can later nudge it further. The bands say nothing about power rating or temperature coefficient either. A multimeter reading is the only way to know what a specific part measures right now.
How is a five-band resistor different from the four bands this calculator uses?
A five-band resistor adds a third significant digit before the multiplier, so three color bands set the number instead of two, and precision parts commonly carry a tighter tolerance color such as brown (±1%) or red (±2%) as the fifth band. Reading a five-band part as though it were four bands misplaces the multiplier by a factor of ten. Count the bands before decoding — this instrument's four fields fit the four-band case only.
Which end of the resistor should I start reading from?
Start from the end furthest from a wider, more isolated band — that gap marks the tolerance band and belongs at the finish, not the start. Genuine parts never open on gold or silver, since neither is a valid first digit, so a sequence that starts with either has been read backwards. On worn or unmarked parts, try a multimeter reading against both directions; only one will land inside a plausible tolerance range.