Sig Fig Subtraction Calculator
Subtract sig figs the right way: this free calculator subtracts two measurements and rounds the result to the correct precision using the subtraction rule (fewest decimal places, not fewest sig figs). Includes catastrophic cancellation analysis when the inputs are close.
Enter Values
The number to subtract from
The number to subtract
Result
Enter values above and click Calculate to see your result.
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Formula
How it works: When subtracting, the result is rounded to the same decimal place as the measurement with the fewest decimal places, following the same rule as addition.
Review and Methodology
This calculator runs locally in your browser. Inputs are converted into the units required by the formula, and the result is paired with supporting references so you can verify the method before using it for planning or estimates.
Worked Example
Sig Fig Rule for Subtraction
Subtraction follows the same significant figures rule as addition. The result is rounded to the decimal place of the measurement with the fewest decimal places. This is especially important in subtraction because subtracting two close values can dramatically reduce the number of meaningful sig figs.
- Subtraction uses the decimal places rule, identical to addition
- Subtracting similar values causes "catastrophic cancellation," which can reduce sig figs significantly
- Example: 5.67 - 5.64 = 0.03, which has only 1 sig fig even though both inputs had 3
- This loss of precision is a real measurement concern, not just an arithmetic technicality
Understanding precision loss in subtraction is critical in experimental science. When two measurements are nearly equal, their difference has much less precision than either individual measurement.
You can also calculate changes using our Sig Fig Addition Calculator, Sig Fig Rules Calculator or Sig Fig Division Calculator.
Frequently Asked Questions
Why can subtraction reduce sig figs so much?
When you subtract two nearly equal numbers, the leading significant digits cancel out, leaving fewer meaningful digits. For example, 23.456 - 23.441 = 0.015, which has only 2 sig figs despite both inputs having 5.
Is this the same rule as addition?
Yes, subtraction and addition use the identical rule: round the result to the same decimal place as the input with the fewest decimal places.
What is catastrophic cancellation?
It is when subtracting two nearly equal numbers causes a dramatic loss of significant figures. Scientists try to avoid experimental designs that rely on small differences between large measurements for this reason.
How do I avoid precision loss in subtraction?
Use instruments with more decimal places, redesign the experiment to measure the difference directly rather than subtracting two large measurements, or use algebraic rearrangements that avoid subtracting similar values.
Does this apply to negative results?
Yes. The rule applies regardless of whether the result is positive or negative. The decimal place of each input still determines the precision of the answer.
Is it possible to embed the Sig Fig Subtraction Calculator on another website?
Yes, embedding the Sig Fig Subtraction Calculator is free. Hit the "Embed" button on this page, adjust the width, height, and theme, then grab the iframe code. It works on WordPress, Wix, Squarespace, Shopify, and plain HTML pages. No registration needed. Full instructions at calculory.com/services/embed-calculators.
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