A resistor color code gives a nominal resistance value, but the actual measured resistance may be higher or lower. The tolerance band defines that permitted variation and produces two useful numbers: the resistor’s minimum resistance and maximum resistance.
Those limits affect circuit calculations that depend on resistance, including branch current, voltage-divider output, bias networks, timing circuits, pull-up and pull-down circuits, and current-limiting resistor selection. A nominal resistor value may be correct for a design while its tolerance range still moves voltage or current outside the acceptable operating window.
Tolerance Band Meaning
The tolerance band is normally the final band on a through-hole resistor. It states how far the actual resistance may vary above or below the decoded nominal value.
Two common tolerance bands are:
| Tolerance band | Tolerance | Meaning |
|---|---|---|
| Gold | ±5% | Actual resistance may be 5% lower or 5% higher than nominal |
| Silver | ±10% | Actual resistance may be 10% lower or 10% higher than nominal |
For example, a resistor decoded as 1,000 ohms with a gold tolerance band is not guaranteed to measure exactly 1,000 ohms. Its acceptable measured value falls within the gold-band resistance range.
Resistance Range Formula
Calculate the resistor tolerance range from the nominal resistance and its tolerance percentage:
\(\displaystyle \text{Minimum Resistance} = \text{Nominal Resistance} \times (1 - \text{Tolerance})\)
\(\displaystyle \text{Maximum Resistance} = \text{Nominal Resistance} \times (1 + \text{Tolerance})\)
Use the tolerance as a decimal in the formula:
- Gold: (5% = 0.05)
- Silver: (10% = 0.10)
The resulting range is the permitted manufacturing variation for that resistor’s marked value.
Gold and Silver Example
Consider the same nominal resistor value: 1.0 kOhm.
1.0 kOhm With Gold Tolerance
A gold band indicates ±5% tolerance.
\(\displaystyle \text{Minimum} = 1{,}000\ \Omega \times (1 - 0.05) = 950\ \Omega\)
\(\displaystyle \text{Maximum} = 1{,}000\ \Omega \times (1 + 0.05) = 1{,}050\ \Omega\)
Gold-band range: 950 ohms to 1,050 ohms
1.0 kOhm With Silver Tolerance
A silver band indicates ±10% tolerance.
\(\displaystyle \text{Minimum} = 1{,}000\ \Omega \times (1 - 0.10) = 900\ \Omega\)
\(\displaystyle \text{Maximum} = 1{,}000\ \Omega \times (1 + 0.10) = 1{,}100\ \Omega\)
Silver-band range: 900 ohms to 1,100 ohms
| Nominal resistance | Tolerance band | Minimum resistance | Maximum resistance | Total range |
|---|---|---|---|---|
| 1.0 kOhm | Gold, ±5% | 950 ohms | 1,050 ohms | 100 ohms |
| 1.0 kOhm | Silver, ±10% | 900 ohms | 1,100 ohms | 200 ohms |
A silver-tolerance resistor permits twice as much variation around the same nominal resistance as a gold-tolerance resistor.
Circuit Calculation Effect
Resistance tolerance can change calculated circuit current. For a fixed supply voltage, lower resistance produces higher current and higher resistance produces lower current.
Using Ohm’s law:
\(\displaystyle I = \frac{V}{R}\)
If a 1.0 kOhm resistor with gold tolerance is connected across 10 V, its possible current range is:
\(I_{\text{minimum resistance}} = \frac{10\ V}{950\ \Omega} = 10.53\ mA\)
\(I_{\text{maximum resistance}} = \frac{10\ V}{1{,}050\ \Omega} = 9.52\ mA\)
The nominal current is 10 mA, but the actual resistor tolerance permits approximately 9.52 mA to 10.53 mA.
Use the Resistor Color Code Calculator to decode the nominal resistance and tolerance band. Then use the Ohm’s Law Calculator with the minimum and maximum resistance values when checking the resulting current, voltage, or power conditions.
Tolerance Limits
A tolerance band describes the allowed variation from the marked resistance value. It does not state:
- Resistor wattage or power rating
- Temperature drift
- Long-term resistance stability
- Pulse capability
- Voltage rating
- Whether the resistor is suitable for a specific circuit or installation
A resistor can fall within its marked tolerance range and still be unsuitable if its power rating, temperature performance, voltage capability, or circuit operating conditions are inadequate.