Significant Figures Calculator

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Significant Figures Calculator
Count Significant FiguresAddition / SubtractionMultiplication / Division
Results:
function toggleInputs(){var mode=document.getElementById('calc_mode').value;var row2=document.getElementById('row2′);if(mode==='count'){row2.style.display='none';}else{row2.style.display='table-row';}}function getSigFigs(n){var s=n.trim().replace(/^-/,");if(s==="")return 0;if(s.indexOf('.')!==-1){var parts=s.split('.');var whole=parts[0].replace(/^0+/,");var frac=parts[1];if(whole===""){var firstNonZero=frac.search(/[1-9]/);return firstNonZero===-1?0:frac.length-firstNonZero;}return whole.length+frac.length;}else{var cleaned=s.replace(/^0+/,");if(cleaned==="")return 0;var trailingZeros=cleaned.match(/0+$/);if(trailingZeros)return cleaned.length-trailingZeros[0].length;return cleaned.length;}}function getDecimalPlaces(n){var s=n.trim();if(s.indexOf('.')===-1)return 0;return s.split('.')[1].length;}function calculateSigFigs(){var mode=document.getElementById('calc_mode').value;var v1=document.getElementById('input1').value;var v2=document.getElementById('input2').value;var ansDiv=document.getElementById('answer');var mainRes=document.getElementById('mainResult');var detailRes=document.getElementById('details');if(v1===""||(mode!=='count'&&v2==="")){alert('Please enter valid numbers');return;}ansDiv.style.display='block';if(mode==='count'){var count=getSigFigs(v1);var num=parseFloat(v1);mainRes.innerHTML="Significant Figures: "+count;detailRes.innerHTML="Number: "+v1+"
Scientific Notation: "+num.toExponential()+"
Precision: "+count+" significant digit(s).";}else if(mode==='add'){var num1=parseFloat(v1);var num2=parseFloat(v2);var dp1=getDecimalPlaces(v1);var dp2=getDecimalPlaces(v2);var limit=Math.min(dp1,dp2);var res=num1+num2;mainRes.innerHTML="Result: "+res.toFixed(limit);detailRes.innerHTML="Number 1 Decimals: "+dp1+"
Number 2 Decimals: "+dp2+"
Rule: Round to the least number of decimal places ("+limit+").
Unrounded: "+(num1+num2);}else if(mode==='multiply'){var num1=parseFloat(v1);var num2=parseFloat(v2);var sf1=getSigFigs(v1);var sf2=getSigFigs(v2);var limit=Math.min(sf1,sf2);var res=num1*num2;mainRes.innerHTML="Result: "+res.toPrecision(limit);detailRes.innerHTML="Number 1 Sig Figs: "+sf1+"
Number 2 Sig Figs: "+sf2+"
Rule: Round to the least number of significant figures ("+limit+").
Unrounded: "+(num1*num2);}}

Calculator Use

The significant figures calculator is a professional-grade tool designed for students, engineers, and scientists to accurately identify and calculate the precision of numerical values. This tool ensures that your mathematical operations maintain scientific integrity by following the standard rules of significant digits (sig figs).

Whether you are performing complex laboratory calculations or simply checking your homework, this calculator handles counting, addition, subtraction, multiplication, and division while applying rounding rules automatically.

Calculation Mode
Choose between counting digits, performing arithmetic with decimal place rules, or arithmetic with sig fig rules.
Input Number(s)
Enter the measurement values. The calculator recognizes decimals, whole numbers, and leading/trailing zeros.
Show Details
Toggle this to see the scientific notation and the specific rules applied to your calculation.

The 5 Rules of Significant Figures

When using the significant figures calculator, the logic is based on these fundamental scientific rules:

  • Non-zero digits: All digits from 1-9 are always significant (e.g., 543 has 3 sig figs).
  • Sandwich Zeros: Zeros between non-zero digits are significant (e.g., 503 has 3 sig figs).
  • Leading Zeros: Zeros to the left of the first non-zero digit are NEVER significant; they are just placeholders (e.g., 0.005 has 1 sig fig).
  • Trailing Zeros with a Decimal: Zeros at the end of a number that contains a decimal point are significant (e.g., 45.00 has 4 sig figs).
  • Trailing Zeros without a Decimal: In a whole number like 100, trailing zeros are generally NOT significant unless specified by scientific notation or a trailing decimal point.

Arithmetic Rules

Addition & Subtraction: The result is rounded to the same number of decimal places as the measurement with the fewest decimal places.

Example: 12.11 + 18.0 = 30.11 → Rounded to 30.1 (one decimal place)

Multiplication & Division: The result is rounded to the same number of significant figures as the measurement with the fewest significant figures.

Example: 4.56 × 1.4 = 6.384 → Rounded to 6.4 (two sig figs)

Calculation Example

Scenario: You are calculating the density of a liquid where the mass is 12.00g and the volume is 3.5mL.

Step-by-step solution:

  1. Identify Sig Figs in Mass: 12.00 has 4 sig figs (trailing zeros with decimal count).
  2. Identify Sig Figs in Volume: 3.5 has 2 sig figs.
  3. Apply Operation: 12.00 / 3.5 = 3.42857…
  4. Rule: Round to the lowest number of sig figs (2).
  5. Result: 3.4 g/mL

Common Questions

Are exact numbers significant?

Exact numbers (like "12 eggs" or the "2" in the formula for circumference) have an infinite number of significant figures. They do not limit the precision of a calculation.

What if a number is in scientific notation?

In scientific notation (e.g., 4.50 x 10^3), all digits in the coefficient are significant. In this case, there are 3 significant figures.

How does this calculator handle rounding?

The significant figures calculator uses standard rounding rules: if the digit following your last significant figure is 5 or greater, round up; otherwise, keep the digit as is.

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