Significant Figures Calculator
Round values and combined measurements to proper precision for physics labs
Parameters
Controls
Calculated Values
Examples
3.14 × 2.1
Two sig figs × two sig figs → two sig figs in product.
- Product:
100.1 + 0.23
One decimal + two decimals → one decimal in sum.
- Sum:
Round π to 3 sig figs
3.14159 → 3.14
- Rounded:
Visualization
Significant Figures in Physics
Significant figures (sig figs) communicate measurement precision when a formal uncertainty is not written. All digits known with confidence, plus one estimated digit, are significant.
Non-zero digits are always significant. Zeros between non-zero digits are significant (e.g. 1002 has four). Leading zeros are not significant; trailing zeros after a decimal point are (e.g. 0.0500 has three).
After multiplication or division, the result cannot be more precise than the least precise factor — keep the same number of sig figs as the input with the fewest.
After addition or subtraction, round to the least number of decimal places among the terms. This is because absolute precision, not relative, limits the sum (e.g. 100.1 + 0.23 → 100.3).
Exact counting numbers (e.g. 3 sides of a triangle) have unlimited sig figs and do not limit products. Constants from tables should be carried with one extra digit during calculation, then rounded at the end.
Sig fig rules are a classroom convention. University labs increasingly require explicit uncertainties from Error Propagation; both skills are complementary.
Key Concepts
- Sig figs = reliable digits + one doubtful digit
- Multiply/divide: result sig figs = min(inputs)
- Add/subtract: match least decimal place
- Leading zeros never count; trailing zeros after decimal do
- Round only the final answer, not every intermediate step
Real-World Applications
- Reporting meter stick readings to 0.001 m
- Calculating area from length and width measurements
- Combining repeated trial averages in intro labs
- Presenting calculator results in AP/IB exam style
Explore Further
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Apply propagated uncertainties to kinematics and force experiments.
- Physics Constants Reference
SI values for c, G, k_B, ε₀, and more used across solvers.
More measurement uncertainty tools
- Error Propagation
Combine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.
- Chi-Square Fit
Compute χ² and reduced χ² to test whether data agree with a physics model within uncertainty.
Physics Equations
Step-by-Step Solution
See how the main results are calculated.
Step 1: Identify the first uncertain digit
Target: 3 significant figures in 3.14159.
Result:
Explanation:
The last significant digit is the one you estimate when reading a scale.
Step 2: Determine the rounding position
Express value in scientific form to see which digit to round.
Equation:
Explanation:
Round at the nth significant digit from the leftmost non-zero digit.
Step 3: Apply rounding
Standard rounding rules: ≥5 rounds up the previous digit.
Calculation:
Result:
Step 4: Verify
Confirm the result has exactly the requested number of sig figs.
Result:
Frequently Asked Questions (FAQ)
Does uncertainty replace sig figs?
Formal labs often report value ± uncertainty. Sig fig rules are a quick convention; use Error Propagation for quantitative σ.
How many sig figs in 0.00450?
Three — leading zeros are not significant; the trailing zero after the decimal is.
Should I round intermediate steps?
Keep extra digits during calculation; round only the final reported value to avoid round-off error accumulation.
Practice MCQs
- 6.2 × 0.84 has how many sig figs in the answer?
- How many significant figures in 0.00450?
- 12.5 + 0.03 should be reported as:
- A calculator displays 4.1837291 from two 3-sig-fig inputs. You should report:
- Which value has the most significant figures?
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