How do I use this calculator?
Choose one of three solves. This calculator defines full-scale span as upper endpoint minus lower endpoint; confirm that the instrument datasheet uses that basis for its percent-FS specification.
Calculator Operations:
- For the absolute error limit, enter the lower and upper range endpoints and the stated percent-FS limit.
- For the percentage, enter both range endpoints and a nonnegative absolute error limit.
- For span and upper endpoint, enter the lower endpoint, a positive absolute error limit and a positive percentage.
An optional indicated reading within the entered or calculated range adds the specification-limit band and the error limit as a percent of the reading magnitude. At a reading of zero, that relative percentage is undefined.
Use the calculate button when all known values have been entered and use the reset button when you want to clear the values from the calculator.
Calculate a percent-of-span error limit, its stated percentage, or the span and upper endpoint, including bipolar ranges. Here FS means upper minus lower; check the datasheet definition. The result is a specification limit, not a complete measurement-uncertainty estimate.
- All Physics Calculators
- Percentage Accuracy Calculator
- Accuracy Calculator
- Reading Accuracy Rate Calculator
Full-Scale Accuracy Formula
This calculator converts a stated percent-of-span specification into a nonnegative absolute error-limit magnitude in the same units as the range. It defines FSV = upper endpoint − lower endpoint. Manufacturers may use full scale, span, selected range or full-scale reading differently, especially for bipolar ranges; confirm the reference value and conditions in the instrument datasheet before using this model.
- FSA
- Nonnegative error-limit magnitude; the associated specification is ±FSA. This is not a measured error or a complete uncertainty estimate.
- A
- Nonnegative stated percent of span, entered as a percent value. A must be positive when solving for a positive span.
- FSV
- The positive span used by this calculator: upper endpoint minus lower endpoint, including for bipolar or offset ranges. Upper endpoint = lower endpoint + FSV.
How to Use the Calculator
- Select the unknown and enter the stated percentage as a percent value, such as 0.5 for 0.5%, rather than the fractional value 0.005.
- Use consistent units for the endpoints, error limit and optional reading. The unit selector changes labels only; it does not convert values or temperature offsets.
- Enter endpoints with upper greater than lower for the error or percentage solve. To infer a positive span, enter a positive error limit and percentage. A supplied optional reading must lie within the range; the specification is not assumed to apply outside it.
How to Interpret the Result
For the supplied pure percent-of-span model, ±FSA is the constant specified error limit over the range under the datasheet conditions. It is not a known measurement error, a correction, a confidence interval or a complete uncertainty budget. Other terms or conditions in the actual specification still apply.
- A larger full-scale range produces a larger absolute error for the same percentage accuracy.
- At smaller nonzero reading magnitudes, the same error limit is a larger percent of the reading magnitude; at zero this comparison is undefined.
- The result is an error magnitude, not a correction factor.
Example
Suppose a pressure gauge has a stated ±2% of span limit over a 0 to 500 psi range, so the span used here is 500 psi.
The entered model gives a ±10 psi specification limit throughout that range under the stated datasheet conditions. The following table expresses this limit as a percent of each positive reading; it does not report measured error or total uncertainty.
| Gauge Reading | Absolute Error Band | Error Limit as % of Reading |
|---|---|---|
| 50 psi | ±10 psi | 20% |
| 100 psi | ±10 psi | 10% |
| 250 psi | ±10 psi | 4% |
| 500 psi | ±10 psi | 2% |
Why Full-Scale Accuracy Matters
Two instruments can have the same percentage specification but very different absolute error bands if their full-scale ranges are different. Selecting a range much larger than the process value often reduces practical measurement quality at the low end of the scale.
Because of this, range selection is just as important as the published accuracy percentage.
Full-Scale Accuracy vs. Accuracy of Reading
- Percent of span in this model: the specified absolute error limit is constant across the range.
- Percent of reading: the specified error-limit component scales with the reading magnitude; a real datasheet may combine it with range, digit or other terms.
Use this calculation when the datasheet specifies a pure percent-of-span limit with the same reference span and applicable conditions. It does not automatically evaluate mixed percent-of-reading plus range/digit terms, piecewise limits or a complete measurement-uncertainty budget.
Practical Tips
- Keep units consistent. If the full-scale value is entered in psi, the calculated full-scale accuracy will also be in psi.
- Enter the percentage as a whole percent value. For example, use 0.5 for 0.5%.
- Confirm the datasheet reference span. Enter its lower and upper endpoints, rather than the current reading or an assumed maximum-positive endpoint.
- For otherwise identical percent-of-span limits, a smaller applicable span gives a smaller absolute error-limit component. Check the full specification and operating limits before selecting a range.
- Check whether resolution, hysteresis, temperature and drift are already included in the quoted specification. A measurement-uncertainty evaluation considers the relevant components and their treatment; do not automatically add or double-count them.
