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Count and calculate significant figures with precision
A genuine sig fig engine that counts significant digits, rounds to any precision, and applies the correct rules for addition, subtraction, multiplication and division — instantly, in your browser.
| Input | – |
|---|---|
| Ambiguity | – |
| Scientific notation | – |
| Original | – |
|---|---|
| Sig figs kept | – |
| Scientific form | – |
| Raw calculation | – |
|---|---|
| Governing rule | – |
| Limiting value | – |
Why this calculator
Built to match the rules your textbook actually uses
Every result follows standard significant figures conventions used in chemistry, physics and engineering coursework.
Accurate digit counting
Correctly handles leading zeros, captive zeros, trailing zeros, and scientific notation — no shortcuts.
Real operation rules
Addition and subtraction round to the least number of decimal places; multiplication and division round to the least sig figs.
Instant, client-side
Calculations run in your browser with no server round-trip, so results appear the moment you submit.
Ambiguity control
Toggle how trailing zeros without a decimal point are treated, so you can match your instructor's convention.
Copy & export
Copy any result to your clipboard or download it as a plain text file for your notes or lab report.
Works everywhere
A responsive layout that fits phones, tablets and desktops without any horizontal scrolling.
How it works
From number to answer in three steps
Choose a mode
Count sig figs, round to a target precision, or run an arithmetic operation.
Enter your number(s)
Type a decimal, whole number, or scientific notation — validation checks it as you type.
Submit
The button locks while it works, then the page scrolls straight to your result.
Copy or download
Grab the answer instantly, or export it as a text file for later.
Where this matters
Significant figures across the sciences
The same counting and rounding rules show up everywhere measurements meet calculation.
Lab measurements & stoichiometry
Sig figs keep reported concentrations, yields, and titration volumes honest about how precisely they were actually measured.
Example: 25.4 mL read from a graduated cylinder with ±0.1 mL precision must be reported to 3 sig figs, not padded with false precision.
Experimental precision
Derived quantities like acceleration or velocity can never claim more precision than the raw measurements that produced them.
Example: Timing a falling object to 2 sig figs limits any calculated value of g to 2 sig figs too, however many decimals the calculator shows.
Design tolerances
Stress calculations, load ratings, and material specs rely on sig figs to communicate exactly how tight a tolerance really is.
Example: A beam rated to 2 sig figs of load capacity signals a real margin of uncertainty engineers must design around.
Practice
Test yourself
Three quick problems to check your understanding — pick an answer to see instant feedback.
Problem 1 — Counting sig figs
How many significant figures are in the number 0.00340?
Problem 2 — Addition rule
What is 23.45 + 1.2, rounded with the correct number of significant figures?
Problem 3 — Multiplication rule
What is 4.2 × 3.156, rounded with the correct number of significant figures?
What are significant figures?
Significant figures, often shortened to sig figs, are the digits in a measured or calculated number that carry real meaning about how precisely that value is known. Every digit that was actually measured is significant, while digits added only to hold a decimal place are not. A ruler marked in millimetres lets you read a length to the nearest tenth of a millimetre, and every digit you write down within that certainty is significant. Understanding sig figs matters because it stops a calculation from claiming more precision than the original measurements actually support, which is why the concept shows up constantly in chemistry labs, physics coursework, engineering tolerances, and any field where numbers come from instruments rather than exact counts.
The core significant figures rules
A handful of rules cover almost every case you will run into. Non-zero digits are always significant, so 217 has three significant digits no matter what. Zeros trapped between two non-zero digits, sometimes called captive zeros, are also always significant, which is why 405 has three sig figs. Leading zeros, the ones that appear before the first non-zero digit, are never significant because they only locate the decimal point rather than measuring anything, so 0.0032 has just two significant digits, the 3 and the 2. Trailing zeros are the trickiest case: when a decimal point is present, trailing zeros are significant, so 3.400 has four sig figs because someone deliberately recorded the precision down to the thousandths place. Without a decimal point, trailing zeros are ambiguous, so a number like 1500 is usually read as having two significant figures unless it is written with a decimal point, a bar over the zero, or in scientific notation to remove the ambiguity.
Why scientific notation removes the guesswork
Scientific notation is the cleanest way to state significant figures without any ambiguity at all, because every digit in the mantissa is understood to be significant. Writing 1.50 × 10³ instead of plain 1500 tells the reader with certainty that three digits were measured, not just estimated from context. This is exactly why lab reports and engineering specifications often favour scientific notation for any value where trailing zeros would otherwise be unclear.
Sig fig rules for addition and subtraction
When adding or subtracting measured values, the result can only be as precise as the least precise measurement involved, and precision here is measured in decimal places rather than total digit count. If you add 12.11, 18.0, and 1.013, the answer is limited by 18.0, which only has one digit after the decimal point, so the raw sum of 31.123 must be rounded to 31.1. This rule exists because a measurement recorded to the nearest tenth cannot suddenly produce a sum accurate to the nearest thousandth just because other numbers in the equation were more precise.
Sig fig rules for multiplication and division
Multiplication and division follow a different logic: the result is limited by the measurement with the fewest total significant figures, regardless of where the decimal point sits. Multiplying 4.56 by 1.4 gives a raw product of 6.384, but because 1.4 only carries two significant figures, the properly reported answer rounds to 6.4. The same principle applies to division, where the quotient inherits the significant-figure count of the least precise input, not the most precise one.
Common examples of significant figures
| Number | Significant figures | Reason |
|---|---|---|
| 0.00420 | 3 | Leading zeros don't count; trailing zero after a decimal does. |
| 7,050 | 3 (ambiguous) | Captive zero counts; trailing zero without a decimal is ambiguous. |
| 3.0500 | 5 | Every digit after a decimal point with a non-zero lead is significant. |
| 6.02 × 10²³ | 3 | Only mantissa digits count in scientific notation. |
| 100. | 3 | A trailing decimal point removes trailing-zero ambiguity. |
How to use a significant figures calculator effectively
The fastest way to check your own work is to type the exact number as it was written in your data, including trailing zeros and decimal points, since removing them changes the answer. For rounding, decide first how many sig figs the least precise measurement in your problem allows, then round your final answer to match, rather than rounding intermediate steps along the way, which can introduce small errors that compound. For addition, subtraction, multiplication, and division, always identify the limiting measurement before you calculate, since that single value decides how much precision your final answer is allowed to claim.
Sig fig rules for logarithms and exponents
Two less common but exam-relevant cases round out the rule set. For logarithms, only the digits after the decimal point in the result (the mantissa) count as significant, and that count should match the significant figures in the original number — so log(4.31 × 10⁴), with three sig figs going in, should be reported with three digits after the decimal point. For exponentiation, such as raising a measured value to a power, the result keeps the same number of significant figures as the base being raised, since the exponent itself is usually treated as an exact, not measured, value.
Why this tool
Built for accuracy other calculators skip
| Feature | This calculator | Basic calculators | Other sig fig tools |
|---|---|---|---|
| Accurate counting of leading-zero decimals (0.00X) | ✓ | ✕ | ✓ |
| Scientific notation input (e-notation and ×10ⁿ) | ✓ | ✕ | ✓ |
| Digit-by-digit explanation of the count | ✓ | ✕ | ✕ |
| Addition/subtraction with sig fig rounding | ✓ | ✕ | ✓ |
| Multiplication/division with sig fig rounding | ✓ | ✕ | ✓ |
| Calculation history | ✓ | ✕ | ✕ |
| Practice problems | ✓ | ✕ | ✓ |
| Free, no sign-up | ✓ | ✓ | ✓ |
FAQ
Common significant figures questions
Written plainly as 100, this has 1 significant figure because the trailing zeros are ambiguous without a decimal point. Written as 100. it has 3 significant figures, and 1.00 × 10² also has 3.
0.005 has 1 significant figure. Leading zeros before the first non-zero digit are placeholders and never count, so only the 5 is significant.
10.0 has 3 significant figures. Because a decimal point is present, the trailing zero after it is no longer ambiguous — it shows the value was measured to that precision.
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