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Significant Figures Calculator and Unit Converter
In short: This significant figures calculator counts sig figs and shows the rule for every digit, rounds to any number of significant figures, does arithmetic with the correct rules for addition, multiplication, logs and pH, writes numbers in scientific notation and converts chemistry units without losing precision. It is free and works in your web browser.
Type a number to count its significant figures. Green digits are significant, grey are not and amber are ambiguous. Use Calculate for a whole sum, such as (25.0 - 23.42) / 4.18, to see the rule applied at each step, and Unit converter for pressure, temperature, energy, concentration, length, mass and volume.
You can type 1.20e3, 1.20 × 10^3 or 1.20*10^3. Hover over or tap a digit to see its rule.
Rounding is done on the digits you type, so values like 2.675 round correctly to 2.68.
Significant figure rules
| Rule | Example | Sig figs |
|---|---|---|
| Non-zero digits always count | 4.56 | 3 |
| Zeros between non-zero digits count | 1.007 | 4 |
| Leading zeros never count | 0.0045 | 2 |
| Trailing zeros count with a decimal point | 2.500, 1500. | 4, 4 |
| Trailing zeros without a decimal point are ambiguous | 1500 | 2 (could be 3 or 4) |
| Scientific notation: count the mantissa only | 6.022 × 10²³ | 4 |
| Exact numbers are unlimited | 12 eggs, 1 L = 1000 mL | ∞ |
Rules for calculations
+ and −: round to the fewest decimal places × and ÷: round to the fewest significant figures
log x: decimal places of the answer = sig figs of x 10^x or e^x: sig figs of the answer = decimal places of x
Keep all digits in the middle of a calculation and round only the final answer. Rounding at each step adds rounding error. When a calculation mixes rules, apply them step by step in the order you would work it out.
Exact conversion factors
| Quantity | Defined relationships |
|---|---|
| Pressure | 1 atm = 101 325 Pa = 760 torr; 1 bar = 100 kPa; 1 mmHg = 133.322 Pa; 1 psi = 6894.76 Pa |
| Temperature | K = °C + 273.15; °F = °C × 9/5 + 32 |
| Energy | 1 cal = 4.184 J; 1 eV = 1.602 176 634 × 10⁻¹⁹ J |
| Length | 1 Å = 0.1 nm = 100 pm = 10⁻¹⁰ m |
| Mass and volume | 1 lb = 453.592 37 g; 1 mL = 1 cm³; 1 L = 1 dm³ |
Worked examples
Counting
0.004050: leading zeros do not count; 4, 0, 5 and the trailing 0 do.
4 significant figures (4.050 × 10⁻³)
Addition
12.11 + 18.0 + 1.013 = 31.123. 18.0 has only one decimal place.
31.1
Multiplication
3.0 × 4.56 = 13.68. 3.0 has only two significant figures.
14
Mixed operations
(25.0 − 23.42) ÷ 4.18: the subtraction gives 1.58, good to one decimal place, so 1.6 (2 sig figs). 1.58 ÷ 4.18 = 0.378.
0.38
pH from concentration
[H⁺] = 2.5 × 10⁻³ M has 2 sig figs. −log(2.5 × 10⁻³) = 2.602.
pH = 2.60 (2 decimal places)
Concentration from pH
pH 4.75 has 2 decimal places. 10⁻⁴·⁷⁵ = 1.778 × 10⁻⁵.
[H⁺] = 1.8 × 10⁻⁵ M
Unit conversion
25.0 °C + 273.15 (exact) = 298.15. Keep one decimal place.
298.2 K
Rounding with a 5
Round 149.5 to 3 sig figs. The dropped digit is 5, so round up.
150. or 1.50 × 10²
Common mistakes
- Counting leading zeros. 0.0025 has 2 significant figures, not 5.
- Dropping meaningful trailing zeros. A balance reading of 2.500 g has 4 significant figures. Writing 2.5 g throws away precision.
- Using the sig-fig rule for addition. 100.0 + 0.123 = 100.1, not 100.123 and not 100.0. Addition uses decimal places.
- Rounding at every step. Carry extra digits and round once at the end.
- Counting the digits before the decimal point of a pH. In pH = 2.60, only the 6 and 0 are significant.
- Letting exact numbers limit the answer. The 2 in 2 × 3.45 g (two identical samples) is a count, so the answer is 6.90 g.
- Writing a large rounded number in plain form. 1.50 × 10⁵ is clear; 150 000 is not.
Writing up a lab report? Draw the structures and reactions to go with your numbers in MolDraw, a free online chemical structure editor.
Open MolDraw editorFrequently asked questions
How many significant figures does 0.004050 have?
Four. The three leading zeros only place the decimal point, so they do not count. The 4, the captive 0, the 5 and the trailing 0 after the decimal point all count. In scientific notation it is 4.050 × 10⁻³.
Are trailing zeros significant?
Trailing zeros are significant when the number has a decimal point, as in 2.500 (4 significant figures) or 1500. (4). In a whole number with no decimal point, such as 1500, they are ambiguous: it could have 2, 3 or 4. Scientific notation removes the doubt: 1.50 × 10³ has 3.
How do I round a number to 3 significant figures?
Start counting at the first non-zero digit, keep three digits and look at the next one. If it is 5 or more, round up. 0.0045678 becomes 0.00457 and 149 500 becomes 150 000, written 1.50 × 10⁵ to show the 3 significant figures.
What are the significant figure rules for addition and multiplication?
For addition and subtraction, round the answer to the fewest decimal places: 12.11 + 18.0 + 1.013 = 31.1. For multiplication and division, round to the fewest significant figures: 3.0 × 4.56 = 14.
How many decimal places should a pH value have?
As many as the significant figures in the hydrogen ion concentration. The digits before the decimal point of a log only give the power of ten. [H+] = 2.5 × 10⁻³ M (2 significant figures) gives pH = 2.60, with 2 decimal places.
Do exact numbers limit the significant figures of an answer?
No. Counted numbers, such as 2 in 2H2O or 5 trials, and defined values, such as 1 kg = 1000 g or 0 °C = 273.15 K, have unlimited significant figures. Only measured values limit the answer.
Does converting units change the number of significant figures?
No. A conversion factor that is defined, such as 1 atm = 101.325 kPa, is exact, so the answer keeps the significant figures of the measurement: 1.00 atm = 101 kPa. For temperature offsets, keep the decimal places: 25.0 °C = 298.2 K.
Related chemistry tools
Want the full method with more examples? Read the significant figures rules guide. Need to sketch molecules for a report? Draw chemical structures online with MolDraw.
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