Significant Figures Calculator

About Significant Figures Calculator

Count significant figures in any number, round to a specific number of sig figs, or perform arithmetic with automatic sig fig rules applied. Each digit is colour-coded to show whether it is significant, with hover tooltips explaining the rule for each digit.

The Five Rules for Significant Figures

Rule	Example	Sig Figs
All non-zero digits are significant	1234	4
Zeros between non-zero digits ("captive zeros") are significant	1002	4
Leading zeros are never significant	0.0045	2
Trailing zeros after a decimal point are significant	3.200	4
Trailing zeros in a whole number are ambiguous (not significant by convention unless marked)	1200	2 (or 4 if written as 1200.)

Counting Examples

Number	Sig Figs	Explanation
45.6	3	All non-zero digits
0.00320	3	Leading zeros don't count; trailing zero after decimal does (3, 2, 0)
100.0	4	1, 0, 0 are captive/trailing after non-zero; trailing 0 after decimal counts
5.00 x 10³	3	Scientific notation makes it clear: 5, 0, 0
0.0102	3	Leading zeros don't count; captive zero between 1 and 2 counts (1, 0, 2)
8000	1	Trailing zeros in whole numbers are ambiguous; default is 1 sig fig
8.000 x 10³	4	Scientific notation clarifies all four digits are significant

Sig Fig Rules for Arithmetic

The rules differ for addition/subtraction vs multiplication/division:

Operation	Rule	Example
Addition/Subtraction	Result has the fewest decimal places of any input	12.52 + 1.3 = 13.8 (1 decimal place)
Multiplication/Division	Result has the fewest sig figs of any input	4.56 x 1.4 = 6.4 (2 sig figs)

Worked example (multiplication): 3.24 x 2.1

• 3.24 has 3 sig figs, 2.1 has 2 sig figs
• Raw result: 6.804
• Round to 2 sig figs: 6.8

Worked example (addition): 103.25 + 0.4

• 103.25 has 2 decimal places, 0.4 has 1 decimal place
• Raw result: 103.65
• Round to 1 decimal place: 103.7

How to Round to N Significant Figures

To round 0.004735 to 2 sig figs:

1. Count from the first non-zero digit: 4, 7 (two sig figs)
2. Look at the next digit (3): it is less than 5, so round down
3. Result: 0.0047

To round 123,456 to 3 sig figs:

1. Count the first three digits: 1, 2, 3
2. Look at the next digit (4): less than 5, round down
3. Result: 123,000

Why Significant Figures Matter

Sig figs reflect measurement precision. If you measure a length with a ruler marked in millimetres, your measurement has precision to 1 mm (three sig figs for a measurement like 15.3 cm). Reporting it as 15.300000 cm would falsely imply precision to nanometres.

In chemistry and physics labs, getting sig figs right is essential because:

• They communicate the precision of your instruments
• Performing calculations with more sig figs than your measurements justify gives a false sense of accuracy
• Lab reports lose marks for incorrect sig fig handling
• Engineering tolerances depend on understanding measurement precision

Scientific Notation and Sig Figs

Scientific notation resolves the ambiguity of trailing zeros in whole numbers:

Standard Form	Scientific Notation	Sig Figs
4500 (ambiguous)	4.5 x 10³	2
4500 (ambiguous)	4.50 x 10³	3
4500 (ambiguous)	4.500 x 10³	4

For calculating how far off a measurement is, the percent error calculator computes absolute and relative error. For working with scientific notation directly, the scientific notation calculator handles conversions and arithmetic.

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