The Resistor Calculator reads colour-band codes into resistance and tolerance, converts a target ohm value into band colours, and combines resistors in series or parallel. Four-band and five-band parts are supported, with an optional conductor mode that applies R = ρL/A for wire resistance from resistivity, length and cross-section.
Read a resistor colour code
Through-hole resistors encode digits, a multiplier and a tolerance as coloured bands. On a four-band part the first two bands are digits, the third is the multiplier and the fourth is tolerance. Read from the end nearest the tolerance band, often gold or silver and set apart by a slight gap.
| Colour | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | ×1 | n/a |
| Brown | 1 | ×10 | ±1% |
| Red | 2 | ×100 | ±2% |
| Orange | 3 | ×1,000 | n/a |
| Yellow | 4 | ×10,000 | n/a |
| Green | 5 | ×100,000 | ±0.5% |
| Blue | 6 | ×1,000,000 | ±0.25% |
| Violet | 7 | ×10,000,000 | ±0.1% |
| Grey | 8 | ×100,000,000 | ±0.05% |
| White | 9 | ×1,000,000,000 | n/a |
| Gold | n/a | ×0.1 | ±5% |
| Silver | n/a | ×0.01 | ±10% |
The Resistor Calculator maps each selected colour to that table and multiplies digit value by the multiplier. A missing tolerance band is treated as ±20% on older parts. Body colour is not part of the code; only the printed bands count. Faded bands and varnish tint cause misreads; confirm odd values with a meter when the part is out of circuit.
Convert a resistance value to colour bands
Reverse lookup starts from a target resistance and a tolerance, then finds band colours for the nearest preferred value. Enter ohms (or kΩ / MΩ); the tool snaps to the selected E-series and shows the matching bands so a parts drawer can be stocked without memorising every colour pair.
Not every ohm value exists as a single standard resistor. 1,050 Ω may snap to 1.0 kΩ or 1.1 kΩ depending on the series. E12 and E24 are the usual through-hole preferences; E96 appears on five-band precision parts. Series or parallel combinations fill gaps when a single standard value is not close enough for the design tolerance.
Gold and silver as multipliers produce values below 10 Ω (gold ×0.1) and below 1 Ω (silver ×0.01) on four-band codes. Confirm the reading direction: reversing brown-black-red as red-black-brown yields a different resistance and a wrong stocking choice.
Calculate resistors in series
Series connection places resistors end to end so the same current flows through each part while voltages add. Total resistance is the ordinary sum of the individual resistances. The Resistor Calculator adds every value entered in series mode and can show the share of voltage each part takes when a supply voltage is provided.
R_total = R1 + R2 + R3 + …Two 470 Ω resistors in series total 940 Ω. Ten equal resistors of value R in series total 10R. Series strings raise resistance when a single part is too low, and they raise voltage rating when each resistor sees only a share of the drop (still check power in each part). Power in each equals I²R for the shared current, or V²/R for the voltage across that part alone.
Open-circuit failure of one series part kills the whole string. That property is useful for fusing behaviour in some designs and a nuisance in others; know which failure mode the product needs.
Calculate resistors in parallel
Parallel connection ties both ends of each resistor to the same two nodes so each branch sees the same voltage. Total resistance comes from summing reciprocals, and the result is always lower than the smallest branch. The Resistor Calculator evaluates the reciprocal sum for any number of parallel parts.
1 / R_total = 1/R1 + 1/R2 + 1/R3 + …For two resistors: `` R_total = (R1 × R2) / (R1 + R2) ``
Fixture: two 100 Ω resistors in parallel: `` R_total = (100 × 100) / (100 + 100) = 10,000 / 200 = 50 Ω ``
Equal parallels of value R give R/2 for two, R/3 for three, and so on. Parallel networks share current; the lower-resistance branch carries more. Power still sums across branches for the same voltage. Short-circuit failure of one branch can overload the supply even when the other branches remain intact.
Read a 4-band and a 5-band resistor
Band count changes how many significant digits the code can carry. Four-band parts use two digits, multiplier and tolerance. Five-band parts use three significant digits, multiplier and tolerance, which suits E96 values such as 1.05 kΩ. A sixth band, when present, often encodes temperature coefficient in ppm/°C rather than another digit.
| Style | Band roles |
|---|---|
| 4-band | digit, digit, multiplier, tolerance |
| 5-band | digit, digit, digit, multiplier, tolerance |
| 6-band | as five-band, plus tempco |
Precision metal-film resistors lean five-band. Carbon-film general-purpose parts lean four-band with gold (±5%) or silver (±10%) tolerance. Surface-mount chips use numeric codes instead of colours; this calculator's colour mode does not decode SMD numerals. When bands look ambiguous, measure resistance with power removed rather than guessing between brown and red under poor light.
Decode brown-black-red-gold
The classic teaching example uses brown, black, red and gold in that order from the digit end. Brown contributes digit 1, black contributes digit 0, red multiplies by 100, and gold sets tolerance to ±5%. The decoded nominal value is one kilohm with a permitted window from 950 Ω to 1,050 Ω.
Resistance = 10 × 100 = 1,000 Ω = 1 kΩ
Tolerance band = ±5%
Allowed range = 1,000 × (1 ± 0.05) = 950 Ω to 1,050 ΩResult: 1 kΩ ±5% (950 Ω to 1,050 Ω). The Resistor Calculator should report the same when those four colours are selected in order. Swapping the first two bands (black-brown-red-gold) would read as 01 × 100 = 100 Ω, which is why band order and the tolerance-end rule matter. Colour vision limits are a real failure mode; a second reader or a meter closes the loop.
Calculate the resistance of a conductor
Wire, PCB traces and bus bars follow a different formula from colour bands. Resistance equals resistivity times length divided by cross-sectional area. Enter ρ, L and A in consistent SI units to estimate ohms for a run that has no colour code at all.
R = ρ × L / ACopper resistivity at 20 °C is about 1.68 × 10⁻⁸ Ω·m; aluminium is higher. Longer runs and thinner cross-sections raise R. Temperature raises copper resistance roughly 0.4% per °C near room temperature; precision work uses a temperature coefficient table. This mode estimates conductor resistance, not colour-band decoding. For branch-circuit voltage drop with AWG tables, use the Voltage Drop Calculator, which already folds length, current and gauge into a drop figure.
Power, tolerance and preferred values
Tolerance describes the factory window around the nominal value, not the long-term drift under heat and humidity. A ±5% 1 kΩ part may legally ship at 960 Ω; circuit design should survive the whole window. Preferred number series (E12, E24, E96) space values so relative steps stay roughly even across decades.
Power rating is separate from ohm value. A 1/4 W resistor at 1 kΩ across 12 V dissipates V²/R = 0.144 W and is fine; the same resistor across 48 V is not. The calculator's network modes can show dissipation when voltage or current is supplied; derate further for enclosed or high-ambient boards.
Frequently asked questions
How do you read a four-band resistor?
Read two digit bands, then the multiplier, then tolerance, starting from the end opposite a lone gold or silver tolerance band when the gap is visible. Brown-black-red-gold is 1 kΩ ±5%. Confirm with a meter if colours are worn.
What does gold mean on a resistor?
As a fourth band, gold means ±5% tolerance. As a third band on four-band parts, gold means multiplier ×0.1. Context (band position) decides which meaning applies; the same pigment is reused on purpose.
How do parallel 100 Ω resistors combine?
Two 100 Ω resistors in parallel equal 50 Ω because the product-over-sum formula gives (100 × 100) / 200 = 50. Equal parallels of R give R/n for n identical branches.
How do series resistors combine?
Add the values. Three 220 Ω resistors in series total 660 Ω. Current is identical in each; voltages divide in proportion to resistance when the string is driven from a voltage source.
What is the difference between 4-band and 5-band?
Five-band codes carry three significant digits and suit tighter E-series values. Four-band codes use two digits and remain common on general-purpose through-hole carbon and metal film parts.
Why is the measured value slightly off?
Tolerance allows a manufacturing range; temperature and meter accuracy add more. A ±5% 1 kΩ part may legally read 960 Ω at room temperature and still be in specification.
Can the calculator design a divider?
Series mode gives the total for a string. Ratio voltages need V × R_bottom / (R_top + R_bottom) as a separate step from the raw resistances. Enter the two divider resistors, sum them, then apply that ratio to the supply.
Does colour coding work for surface-mount parts?
No. SMD resistors use numeric markings (often three or four digits). Colour bands are for through-hole axial parts. Use the ohm-value modes of the tool for SMD when the printed code is already decoded to ohms.
What is E24?
E24 is a preferred-number series with 24 values per decade in the classic 5% spacing set. The reverse lookup snaps to the nearest preferred value in the selected series so the band colours match a part that distributors actually stock.
Summary
The Resistor Calculator turns colour bands into ohms and tolerance, maps targets back to colours via E-series values, and combines series sums or parallel reciprocal networks. Brown-black-red-gold decodes to 1 kΩ ±5%; two 100 Ω parts in parallel equal 50 Ω. Conductor mode applies R = ρL/A when the question is wire resistance rather than a marked discrete resistor.