Uncertainty Propagation for Basic Operations
Calculate how uncertainty carries through when one or two measurements are added, subtracted, multiplied, divided, or raised to a power.
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When to use this tool
Use it when a result is obtained directly from one or two measured quantities and you need to report not only the calculated value, but also the uncertainty it inherits. For example, it can estimate the uncertainty of an area calculated as length × width, a density obtained as mass ÷ volume, or the difference between two temperatures. It is designed for one operation at a time and for measurements that can be treated as independent.
How it works
Enter each measurement as value ± uncertainty. You can express uncertainty in the same units as the value (Absolute mode) or as a percentage (Relative mode), then choose the operation. RSS combines the contributions by root sum of squares and is the usual choice when measurements are independent; Conservative adds them directly to provide a more cautious estimate. For a power, the exponent is assumed to be known exactly; if the base range reaches zero, the tool warns you or stops the calculation when the first-order approximation is no longer reliable. The tool returns the calculated value, its standard uncertainty, uncertainty percentage, value ± uncertainty range, and a rounded version for reporting. The approximation may not be suitable when the measurements are related to each other, when more than two quantities are involved, or when uncertainty is so large that the operation is no longer nearly linear.