Scientific Figures Calculator
Use this calculator to perform basic arithmetic operations on two numbers and get the result rounded to the correct number of significant figures or decimal places, according to scientific rules.
Results:
Raw Result:
Result with Scientific Figures:
(Note: Large or very small numbers may be displayed in scientific notation.)
// Function to count significant figures from a string representation of a number
function countSigFigsFromString(numStr) {
numStr = numStr.trim();
if (numStr === "") return 0;
if (numStr === "0") return 1; // Convention for 0
// Handle scientific notation (e.g., "1.23e-4″)
var parts = numStr.split(/e|E/);
var s = parts[0]; // Use mantissa for sig fig count
s = s.replace(/^-/, "); // Remove leading minus sign
// If the number is effectively zero (e.g., "0.0", "0.00")
if (parseFloat(s) === 0 && s.includes('.')) {
return s.length – s.indexOf('.'); // "0.0" -> 2, "0.00" -> 3
}
// Remove leading zeros (e.g., "0.00123" -> "123", "0.123" -> "123")
s = s.replace(/^0+(?=\d)/, ");
// Remove decimal point for counting
s = s.replace(/\./, ");
// If the original mantissa string did NOT contain a decimal, remove trailing zeros
// This handles "1200" -> "12" (2 sig figs)
if (parts[0].indexOf('.') === -1) {
s = s.replace(/0+$/, ");
}
return s.length;
}
// Function to count decimal places from a string representation of a number
function countDecimalPlacesFromString(numStr) {
numStr = numStr.trim();
if (numStr.includes('e') || numStr.includes('E')) { // Handle scientific notation
var parts = numStr.split(/e|E/);
numStr = parts[0]; // Decimal places are determined by the mantissa
}
var decimalIndex = numStr.indexOf('.');
if (decimalIndex === -1) {
return 0;
}
return numStr.length – decimalIndex – 1;
}
// Function to round a number to a specific number of significant figures
function roundToSigFigs(num, sigFigs) {
if (sigFigs <= 0) return num.toString();
if (num === 0) {
// toPrecision(n) for 0 gives "0.00…" with n-1 zeros after decimal.
// This is generally correct for significant figures of zero.
return num.toPrecision(sigFigs);
}
return num.toPrecision(sigFigs);
}
// Function to round a number to a specific number of decimal places
function roundToDecimalPlaces(num, decPlaces) {
return num.toFixed(decPlaces);
}
function calculateSigFigs() {
var num1Str = document.getElementById("firstNumber").value;
var num2Str = document.getElementById("secondNumber").value;
var num1 = parseFloat(num1Str);
var num2 = parseFloat(num2Str);
var operation;
var operations = document.getElementsByName("operation");
for (var i = 0; i < operations.length; i++) {
if (operations[i].checked) {
operation = operations[i].value;
break;
}
}
// Input validation
if (isNaN(num1) || isNaN(num2)) {
document.getElementById("rawResult").textContent = "Error: Please enter valid numbers.";
document.getElementById("finalResult").textContent = "";
return;
}
var rawResult;
var finalResult;
switch (operation) {
case "add":
rawResult = num1 + num2;
var dp1 = countDecimalPlacesFromString(num1Str);
var dp2 = countDecimalPlacesFromString(num2Str);
var minDP = Math.min(dp1, dp2);
finalResult = roundToDecimalPlaces(rawResult, minDP);
break;
case "subtract":
rawResult = num1 – num2;
var dp1 = countDecimalPlacesFromString(num1Str);
var dp2 = countDecimalPlacesFromString(num2Str);
var minDP = Math.min(dp1, dp2);
finalResult = roundToDecimalPlaces(rawResult, minDP);
break;
case "multiply":
rawResult = num1 * num2;
var sf1 = countSigFigsFromString(num1Str);
var sf2 = countSigFigsFromString(num2Str);
var minSF = Math.min(sf1, sf2);
finalResult = roundToSigFigs(rawResult, minSF);
break;
case "divide":
if (num2 === 0) {
document.getElementById("rawResult").textContent = "Error: Division by zero.";
document.getElementById("finalResult").textContent = "";
return;
}
rawResult = num1 / num2;
var sf1 = countSigFigsFromString(num1Str);
var sf2 = countSigFigsFromString(num2Str);
var minSF = Math.min(sf1, sf2);
finalResult = roundToSigFigs(rawResult, minSF);
break;
default:
document.getElementById("rawResult").textContent = "Error: Invalid operation.";
document.getElementById("finalResult").textContent = "";
return;
}
document.getElementById("rawResult").textContent = rawResult.toString();
document.getElementById("finalResult").textContent = finalResult.toString();
}
// Initial calculation on page load with default values
window.onload = calculateSigFigs;
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font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
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max-width: 600px;
margin: 20px auto;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
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.operation-selection {
margin-bottom: 20px;
display: flex;
align-items: center;
flex-wrap: wrap;
gap: 15px;
}
.operation-selection label {
margin-bottom: 0;
font-weight: normal;
cursor: pointer;
display: flex;
align-items: center;
gap: 5px;
}
.operation-selection input[type="radio"] {
margin-right: 5px;
transform: scale(1.2);
}
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background-color: #007bff;
color: white;
padding: 12px 25px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 1.1em;
display: block;
width: 100%;
margin-top: 20px;
transition: background-color 0.3s ease;
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.calculator-inputs button:hover {
background-color: #0056b3;
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background-color: #e9f7ff;
border: 1px solid #b3e0ff;
border-radius: 8px;
padding: 15px 20px;
margin-top: 25px;
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/* Article Styling */
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color: #333;
max-width: 800px;
margin: 40px auto;
padding: 20px;
background-color: #fff;
border-radius: 8px;
box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05);
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font-size: 2em;
margin-bottom: 20px;
text-align: center;
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font-size: 1.5em;
margin-top: 30px;
margin-bottom: 15px;
border-bottom: 1px solid #eee;
padding-bottom: 5px;
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margin-bottom: 15px;
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list-style-type: disc;
margin-left: 25px;
margin-bottom: 15px;
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list-style-type: decimal;
margin-left: 25px;
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Understanding Significant Figures in Scientific Calculations
In scientific measurements and calculations, precision and accuracy are paramount. Significant figures (often abbreviated as sig figs) are a crucial concept that helps scientists and engineers express the reliability and precision of their measurements and the results derived from them. This calculator helps you apply the rules of significant figures to basic arithmetic operations.
What are Significant Figures?
Significant figures are the digits in a number that carry meaning contributing to its precision. This includes all non-zero digits, zeros between non-zero digits, and trailing zeros in a number that contains a decimal point. Leading zeros are never significant.
Rules for Counting Significant Figures:
- Non-zero digits: All non-zero digits are always significant.
- Example:
123.45 has 5 significant figures.
- Example:
789 has 3 significant figures.
- Zeros between non-zero digits (Sandwich Zeros): Zeros located between non-zero digits are significant.
- Example:
1005 has 4 significant figures.
- Example:
2.07 has 3 significant figures.
- Leading Zeros: Zeros that precede all non-zero digits are NOT significant. They merely 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 (at the end of the number):
- With a decimal point: Trailing zeros are significant if the number contains a decimal point.
- Example:
12.00 has 4 significant figures.
- Example:
1.20 has 3 significant figures.
- Example:
120. (with a decimal point) has 3 significant figures.
- Without a decimal point: Trailing zeros in a whole number without an explicitly written decimal point are generally considered ambiguous and are often assumed to be NOT significant unless otherwise specified (e.g., by using scientific notation). For this calculator, we follow the common convention that they are NOT significant.
- Example:
1200 is typically assumed to have 2 significant figures (the 1 and 2).
- Example:
50 is typically assumed to have 1 significant figure.
Rules for Arithmetic Operations:
1. Addition and Subtraction:
When adding or subtracting numbers, the result should be rounded to the same number of decimal places as the measurement with the fewest decimal places.
- Example:
12.34 (2 decimal places)+ 5.6 (1 decimal place)= 17.94 (Raw Result)- The limiting factor is
5.6 with 1 decimal place.
- Final Result:
17.9 (rounded to 1 decimal place)
- Example:
123.567 (3 decimal places)- 1.2 (1 decimal place)= 122.367 (Raw Result)- The limiting factor is
1.2 with 1 decimal place.
- Final Result:
122.4 (rounded to 1 decimal place)
2. Multiplication and Division:
When multiplying or dividing numbers, the result should be rounded to the same number of significant figures as the measurement with the fewest significant figures.
- Example:
12.34 (4 significant figures)× 5.6 (2 significant figures)= 69.104 (Raw Result)- The limiting factor is
5.6 with 2 significant figures.
- Final Result:
69 (rounded to 2 significant figures)
- Example:
1200 (2 significant figures, assuming no decimal)÷ 2.0 (2 significant figures)= 600 (Raw Result)- Both numbers have 2 significant figures.
- Final Result:
6.0 × 10^2 or 600 (if the context allows for ambiguity, but scientifically 6.0 × 10^2 is clearer for 2 sig figs). Our calculator will output 6.0e+2.
How to Use the Calculator:
- Enter your First Number: Type the first value into the "First Number" field. Be mindful of how you enter trailing zeros (e.g.,
1200 vs 1200. vs 1.20e3).
- Enter your Second Number: Type the second value into the "Second Number" field.
- Select an Operation: Choose whether you want to Add, Subtract, Multiply, or Divide.
- Click "Calculate": The calculator will display both the "Raw Result" (the exact mathematical answer) and the "Result with Scientific Figures" (the answer rounded according to the rules of significant figures).
This tool is designed to help students, educators, and professionals quickly verify their calculations and ensure they are reporting results with the appropriate level of precision.