Significant Figures
Rounding
Round a result to match its uncertainty, the way lab reports require. Enter value and ±Δ — get a correctly matched pair with one-line reasoning. No signup, no ads.
01How Rounding Works
Lab convention: round the uncertainty to one significant figure — or two if its leading digit is 1 — then round the measured value to the same decimal place. Never report more decimal places in the result than in the uncertainty.
For the full guide with worked examples, read significant figures for uncertainty.
02Worked Example
KE = 9.00347 ± 0.639 J
Step 1 — Leading digit of 0.639 is 6 → round Δ to 1 sig fig → 0.6 J (tenths place).
Step 2 — Round 9.00347 to the tenths place → 9.0 J.
Result: 9.0 ± 0.6 J.
03Frequently Asked Questions
Q1How do I round a value with its uncertainty?
Round the uncertainty first to 1 significant figure (or 2 if the leading digit is 1). Then round the measured value to the same decimal place as that rounded uncertainty. Report them together as value ± uncertainty.
Q2Why does a leading 1 get two significant figures?
A leading digit of 1 carries less relative precision than 2–9. Rounding 0.014 to 0.01 would change the uncertainty by 40%, so the standard lab convention keeps two figures when the leading digit is 1.
Q3Should I round the result or the uncertainty first?
Always round the uncertainty first. The uncertainty sets the precision; the result is then matched to that decimal place. Rounding the result first can leave mismatched decimal places.
Q4Is this calculator free?
Yes. ΔPropagator tools are free to use, with no signup, no ads, and no paywall.