Significant Figures Calculator
Use this calculator to determine the number of significant figures in a given number or to round a number to a specified number of significant figures.
function countSignificantFigures(numStr) {
numStr = String(numStr).trim();
if (numStr === "" || numStr === "-" || numStr === "+") {
return 0; // Invalid or empty input
}
// Handle scientific notation (e.g., 1.23e-4 -> 1.23)
numStr = numStr.split(/[eE]/)[0];
// Remove leading/trailing signs for counting
numStr = numStr.replace(/^[+-]/, ");
// Special case: "0" has 1 significant figure
if (numStr === "0") {
return 1;
}
var hasDecimal = numStr.indexOf('.') !== -1;
var sigFigs = 0;
var firstNonZeroFound = false;
for (var i = 0; i "00" -> 2 sig figs
// Example: "0.00" -> "000" -> 3 sig figs
// Example: ".0" -> "0" -> 1 sig fig
return numStr.replace('.', ").length;
}
// For numbers without a decimal, trailing zeros are NOT significant
// Example: 1200 has 2 sig figs, not 4
if (!hasDecimal) {
var tempSigFigs = sigFigs;
var tempNumStr = numStr;
while (tempNumStr.length > 0 && tempNumStr[tempNumStr.length – 1] === '0') {
tempNumStr = tempNumStr.slice(0, -1);
if (tempSigFigs > 0) { // Only decrement if we've actually counted digits
tempSigFigs–;
}
}
sigFigs = tempSigFigs;
}
return sigFigs;
}
function roundToSignificantFigures(num, sigFigs) {
var numberValue = parseFloat(num);
if (isNaN(numberValue) || !isFinite(numberValue)) {
return "Invalid Number";
}
if (numberValue === 0) {
return "0";
}
if (sigFigs <= 0) {
return "Rounding to 0 or negative significant figures is not meaningful.";
}
// toPrecision() is the standard JavaScript method for rounding to significant figures.
// It returns a string, potentially in scientific notation.
var roundedString = numberValue.toPrecision(sigFigs);
// Attempt to convert scientific notation to standard form if it doesn't lose precision
if (roundedString.indexOf('e') !== -1) {
var parts = roundedString.split('e');
var mantissa = parts[0];
var exponent = parseInt(parts[1], 10);
var decimalIndex = mantissa.indexOf('.');
if (decimalIndex === -1) {
decimalIndex = mantissa.length;
}
var digits = mantissa.replace('.', '');
var newDecimalIndex = decimalIndex + exponent;
if (newDecimalIndex 0.00123
return "0." + "0".repeat(Math.abs(newDecimalIndex)) + digits;
} else if (newDecimalIndex >= digits.length) {
// e.g., 1.23e+4 -> 12300
return digits + "0".repeat(newDecimalIndex – digits.length);
} else {
// e.g., 12.3e+1 -> 123
return digits.substring(0, newDecimalIndex) + '.' + digits.substring(newDecimalIndex);
}
} else {
return roundedString;
}
}
function calculateSignificantFigures() {
var numberInput = document.getElementById("numberInput").value;
var sigFigsToRoundInput = document.getElementById("sigFigsToRound").value;
var sigFigsCountResult = document.getElementById("sigFigsCountResult");
var roundedNumberResult = document.getElementById("roundedNumberResult");
sigFigsCountResult.innerHTML = "";
roundedNumberResult.innerHTML = "";
if (numberInput.trim() === "") {
sigFigsCountResult.innerHTML = "Please enter a number.";
return;
}
var numSigFigs = countSignificantFigures(numberInput);
sigFigsCountResult.innerHTML = "The number
" + numberInput + " has
" + numSigFigs + " significant figures.";
if (sigFigsToRoundInput.trim() !== "") {
var desiredSigFigs = parseInt(sigFigsToRoundInput, 10);
if (isNaN(desiredSigFigs) || desiredSigFigs <= 0) {
roundedNumberResult.innerHTML = "Please enter a valid positive number for 'Round to Significant Figures'.";
return;
}
var roundedNum = roundToSignificantFigures(numberInput, desiredSigFigs);
roundedNumberResult.innerHTML = "Rounded to
" + desiredSigFigs + " significant figures:
" + roundedNum + "";
}
}
.significant-figures-calculator {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
box-shadow: 0 2px 4px rgba(0,0,0,0.1);
}
.significant-figures-calculator h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
}
.significant-figures-calculator p {
color: #555;
line-height: 1.6;
}
.significant-figures-calculator .calculator-form .form-group {
margin-bottom: 15px;
}
.significant-figures-calculator .calculator-form label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #444;
}
.significant-figures-calculator .calculator-form input[type="text"],
.significant-figures-calculator .calculator-form input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
}
.significant-figures-calculator .calculator-form button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
cursor: pointer;
transition: background-color 0.3s ease;
}
.significant-figures-calculator .calculator-form button:hover {
background-color: #0056b3;
}
.significant-figures-calculator .calculator-results {
margin-top: 25px;
padding-top: 20px;
border-top: 1px solid #eee;
}
.significant-figures-calculator .calculator-results h3 {
color: #333;
margin-bottom: 15px;
text-align: center;
}
.significant-figures-calculator .calculator-results .result-item {
background-color: #e9f7ef;
border: 1px solid #d4edda;
padding: 10px 15px;
border-radius: 4px;
margin-bottom: 10px;
color: #155724;
font-size: 1.1em;
}
.significant-figures-calculator .calculator-results .result-item strong {
color: #0a3622;
}
.significant-figures-calculator .calculator-results .error {
background-color: #f8d7da;
border-color: #f5c6cb;
color: #721c24;
padding: 10px 15px;
border-radius: 4px;
}
Understanding Significant Figures
Significant figures (often called sig figs) are the digits in a number that carry meaning contributing to its precision. They are crucial in scientific and engineering fields to express the reliability of a measurement or calculation. When you perform calculations, the result should not imply greater precision than the least precise measurement used.
Why are Significant Figures Important?
Imagine measuring a length with a ruler marked in millimeters. You might measure an object as 12.5 mm. You can be certain about the '1' and '2', and reasonably estimate the '5'. If you then report it as 12.500 mm, you're implying a precision down to micrometers, which your ruler cannot provide. Significant figures help us communicate the actual precision of our data.
Rules for Counting Significant Figures
Here are the generally accepted rules for determining the number of significant figures in a given number:
- Non-zero digits are always significant.
- Example:
123.45 has 5 significant figures.
- Example:
789 has 3 significant figures.
- Zeros between non-zero digits (captive zeros) are significant.
- Example:
101.12 has 5 significant figures.
- Example:
5003 has 4 significant figures.
- Leading zeros (zeros before non-zero digits) are NOT significant. They only indicate the position of the decimal point.
- Example:
0.00123 has 3 significant figures (the 1, 2, and 3).
- Example:
0.5 has 1 significant figure.
- Trailing zeros (zeros at the end of the number) are significant ONLY if the number contains a decimal point.
- Example:
12.00 has 4 significant figures (the 1, 2, and both zeros).
- Example:
100. (with a decimal point) has 3 significant figures.
- Example:
100 (without a decimal point) has 1 significant figure (the 1). The trailing zeros are ambiguous and generally considered non-significant unless specified.
- Numbers in scientific notation: All digits in the mantissa (the part before "x 10^") are significant.
- Example:
1.23 x 10^4 has 3 significant figures.
- Example:
5.00 x 10^-2 has 3 significant figures.
- Exact numbers: Numbers that are counted or defined (e.g., 12 eggs in a dozen, 100 cm in 1 meter) have an infinite number of significant figures. These are not typically subject to significant figure rules in calculations.
Rules for Rounding to Significant Figures
When rounding a number to a specific number of significant figures, follow these steps:
- Identify the significant figures: Determine which digits are significant based on the rules above.
- Count from the first non-zero digit: Start counting significant figures from the first non-zero digit.
- Look at the next digit:
- If the digit immediately to the right of your desired last significant figure is 5 or greater, round up the last significant figure.
- If it is less than 5, keep the last significant figure as it is.
- Replace remaining digits:
- If the number has a decimal point, drop all digits to the right of the rounded significant figure.
- If the number does NOT have a decimal point, replace any digits between the last significant figure and the decimal point (or end of the number) with zeros to maintain the correct magnitude.
Rounding Examples:
- Round
123.456 to 3 significant figures:
The first three significant figures are 1, 2, 3. The next digit is 4 (less than 5).
Result: 123
- Round
0.007895 to 3 significant figures:
The first three significant figures are 7, 8, 9. The next digit is 5 (5 or greater). Round up the 9.
Result: 0.00790 (the trailing zero is significant because of the decimal)
- Round
12,345 to 2 significant figures:
The first two significant figures are 1, 2. The next digit is 3 (less than 5).
Result: 12,000 (zeros are added to maintain magnitude, but are not significant)
- Round
49.99 to 3 significant figures:
The first three significant figures are 4, 9, 9. The next digit is 9 (5 or greater). Round up the last 9, which propagates.
Result: 50.0 (the trailing zero is significant)
How to Use the Calculator
- Enter a Number: Type the number you want to analyze into the "Enter a Number" field. This can be an integer, a decimal, or a number in scientific notation (e.g.,
1.23e-4).
- (Optional) Round to Significant Figures: If you also want to round the number, enter the desired number of significant figures in the "Round to Significant Figures" field.
- Click "Calculate": The calculator will display the total number of significant figures in your input and, if specified, the number rounded to your desired precision.