Resistor Tolerance: Calculate Limits, Not Just Nominals
How do you calculate resistor tolerance?
Multiply the nominal resistance by the tolerance percentage divided by 100. Subtract that amount for the lower limit and add it for the upper limit: 2,200 Ω ±5% becomes 2,090–2,310 Ω. For a paper calculation involving series resistors, add their resistance limits, not their tolerance percentages. These are tolerance-only bounds, not permission to build or test an electrical circuit.
The nominal value is the specified reference value. Vishay's resistor guide describes tolerance as an allowed percentage deviation from it. A tolerance calculation therefore produces an interval; it does not identify the actual resistance of an individual component.
What goes into the minimum and maximum calculation?
Let R mean nominal resistance and t mean the tolerance percentage written as a number, such as 5. The allowed difference from nominal is R × t ÷ 100. The endpoints are:
- Minimum resistance = R × (1 − t ÷ 100).
- Maximum resistance = R × (1 + t ÷ 100).
For our hypothetical 2,200 Ω resistor, 2,200 × 5 ÷ 100 = 110 Ω. The lower limit is 2,200 − 110 = 2,090 Ω; the upper limit is 2,200 + 110 = 2,310 Ω. The percentage has become a resistance difference with a unit.
Keep the units consistent. Here, 2.2 kΩ means 2,200 Ω. Entering 2.2 for one resistor and 1,000 for another silently mixes kilo-ohms and ohms. Our Ohm's law explanation introduces the resistance symbol and unit alongside voltage and current.
How do different tolerances combine in series?
For the ideal series model, equivalent resistance is the sum of the individual resistances, as shown in Real Analog, chapter 2. Use that relationship with a second hypothetical resistor: 1,000 Ω ±1%, whose allowed difference is 10 Ω.
The following original example treats each resistor's stated endpoints as allowed and considers both reaching their lower or upper endpoint together. It makes no probability claim about manufactured parts.
| Paper example | Nominal | Difference from nominal | Minimum | Maximum |
|---|---|---|---|---|
| R1, ±5% | 2,200 Ω | ±110 Ω | 2,090 Ω | 2,310 Ω |
| R2, ±1% | 1,000 Ω | ±10 Ω | 990 Ω | 1,010 Ω |
| Series total | 3,200 Ω | ±120 Ω | 3,080 Ω | 3,320 Ω |
The total percentage is 120 ÷ 3,200 × 100 = 3.75%. Adding 5% and 1% to obtain 6% would be wrong for this model: those percentages refer to different nominal resistances. Add the differences expressed in ohms, then divide by the combined nominal resistance.
This calculation concerns a series sum. Our loaded voltage-divider guide handles a different question: how a connected load changes a divider's output. Its circuit relationship cannot be replaced with this simple sum.
Would the nominal value pass while the range fails?
Suppose a hypothetical worksheet requires total resistance between 3,100 and 3,300 Ω, inclusive. The nominal total, 3,200 Ω, sits inside that interval. However, the calculated endpoints extend 20 Ω below and above it. The stated tolerance bounds therefore do not guarantee the requirement.
Write that conclusion beside the calculation. “Nominal value passes” and “all allowed values pass” answer different questions. Our verification and validation guide explains how to connect a requirement with appropriate evidence.
For a second paper scenario, change only R1's tolerance to ±1%. Its difference becomes 22 Ω; adding R2's 10 Ω gives ±32 Ω around 3,200 Ω. The new endpoints, 3,168 and 3,232 Ω, fit inside the hypothetical requirement. This changes the mathematical result, but does not establish whether any physical component is suitable for an application.
What does this interval leave out?
It is not a measurement result with an uncertainty statement. NIST's measurement-uncertainty guidance connects uncertainty with the incomplete knowledge associated with measurement. A manufacturer's tolerance alone does not tell you the probability of finding a particular resistance within the interval.
Nor does the interval account for every operating effect. For example, the published Vishay MRS16/MRS25 datasheet lists resistance tolerance and temperature coefficient separately. Do not treat the tolerance percentage as a complete description of temperature-related change.
Keep this exercise on paper. Physical electrical work requires the applicable equipment instructions and a qualified person; these equations provide no wiring, energizing or measurement procedure.