how to calculate a weighted average: interactive calculator & guide
Use this single-column professional calculator to master how to calculate a weighted average, see intermediate math, copy results, and learn the full formula in plain language.
Weighted Average Calculator
Enter the first data point.
Assign its weighting factor (must be positive).
Enter the second data point.
Assign its weighting factor (must be positive).
Enter the third data point.
Assign its weighting factor (must be positive).
Enter an optional fourth data point if needed.
Assign its weighting factor; leave zero if unused.
Enter an optional fifth data point if needed.
Assign its weighting factor; leave zero if unused.
Weighted Average
0.00
Formula: Σ(value × weight) ÷ Σ(weight)
Total of weights: 0.00
Sum of weighted values: 0.00
Simple average (unweighted): 0.00
Normalized leading weight share: 0.00%
This calculation of how to calculate a weighted average multiplies each value by its weight, adds the weighted contributions, and divides by the total of weights. It is the correct way to emphasize more important data points.
Value
Weight
Weighted Contribution
Normalized Weight
Table: Detailed breakdown used to calculate the weighted average.
Blue bars: values; Green bars: weighted contributions scaled; both update in real time to show how to calculate a weighted average visually.
What is how to calculate a weighted average?
Understanding how to calculate a weighted average is essential whenever certain numbers deserve more influence than others. A weighted average emphasizes important observations, such as credit scores with different bureau pull dates, portfolio holdings with different sizes, or project milestones with different impacts.
Professionals who must know how to calculate a weighted average include analysts, investors, CFOs, operations leaders, educators, and anyone blending metrics with unequal importance. Many people think how to calculate a weighted average is the same as adding values and dividing by count, but that misconception ignores the power of weights.
how to calculate a weighted average Formula and Mathematical Explanation
The core steps of how to calculate a weighted average are straightforward but exact. Multiply each value by its assigned weight, sum the products, then divide by the sum of weights. This ensures larger weights push the result toward their values.
List all values that need emphasis.
Assign a weight to each value reflecting its importance.
Compute each value × weight product.
Sum all products to get the weighted total.
Sum all weights.
Divide the weighted total by the sum of weights to finish how to calculate a weighted average.
Variable
Meaning
Unit
Typical range
v
Individual value in how to calculate a weighted average
Any consistent unit
-1,000,000 to 1,000,000
w
Assigned weight for each value
Relative factor
0 to 1000
Σ(v × w)
Sum of weighted contributions
Value × weight
-1e9 to 1e9
Σw
Total of all weights
Relative factor
0.0001 to 1e6
WA
Final result of how to calculate a weighted average
Same as value unit
-1e9 to 1e9
Variable reference for how to calculate a weighted average.
Practical Examples (Real-World Use Cases)
Example 1: Portfolio return
Imagine three funds with returns of 4%, 6%, and 9% and allocation weights of 20, 30, and 50. Multiplying each return by its weight and dividing by total weights shows how to calculate a weighted average portfolio return of 7.4%. This weighted average highlights the dominant 50% position pulling the result upward.
Example 2: Academic grade
A student has assignments (weight 20) at 85, midterm (weight 30) at 78, final (weight 50) at 92. Running how to calculate a weighted average yields (85×20 + 78×30 + 92×50) ÷ 100 = 87.9. The heavier final pushes the overall grade higher because of its larger weight.
How to Use This how to calculate a weighted average Calculator
Enter each value and its weight into the fields.
Watch the results update in real time as you learn how to calculate a weighted average.
Review intermediate totals to confirm Σ weights and Σ weighted values.
Read the highlighted weighted average to see the final answer.
Use the table and chart to confirm the balance of contributions.
Copy results to share your how to calculate a weighted average findings.
Interpret the main result as the center of gravity of your data. If one weight is extremely high, the how to calculate a weighted average output will move toward that value.
Key Factors That Affect how to calculate a weighted average Results
Relative weight scale: A single dominant weight can control how to calculate a weighted average.
Sign of values: Negative values can reduce the total, changing how to calculate a weighted average for risk cases.
Data dispersion: Widely spread values increase sensitivity when you calculate a weighted average.
Weight normalization: Using normalized percentages simplifies how to calculate a weighted average consistently.
Time sensitivity: Recency weighting adjusts how to calculate a weighted average for time series.
Fees or adjustments: After-fee values change the math of how to calculate a weighted average for net results.
Inflation effects: Real terms vs nominal terms alter interpretations of how to calculate a weighted average.
Risk premiums: Heavier weights on risky assets can distort how to calculate a weighted average outcome.
Frequently Asked Questions (FAQ)
Can weights be decimals? Yes, using decimals is valid when you decide how to calculate a weighted average.
Can weights sum to more than 1? Absolutely; how to calculate a weighted average only needs consistent weights and divides by their sum.
What if a weight is zero? That value is ignored in how to calculate a weighted average.
Can values be negative? Yes; negative figures will reduce the result when you calculate a weighted average.
Do weights need to be percentages? No; any positive scale works when applying how to calculate a weighted average.
What if all weights are equal? Then how to calculate a weighted average equals the simple average.
Is rounding important? Rounding after you calculate a weighted average keeps reporting clean; avoid rounding weights beforehand.
How many data points can I use? As many as needed; the principle of how to calculate a weighted average remains the same.
Related Tools and Internal Resources
{related_keywords} – Additional guidance on how to calculate a weighted average applications.
{related_keywords} – Portfolio allocation resource connected to how to calculate a weighted average.
{related_keywords} – Academic grading insights using how to calculate a weighted average.
{related_keywords} – Operational KPIs that rely on how to calculate a weighted average.
{related_keywords} – Risk-weighted metrics showing how to calculate a weighted average under stress.
{related_keywords} – Inflation-adjusted analytics tied to how to calculate a weighted average.
var defaultValues=[50,70,90,0,0];
var defaultWeights=[2,3,5,0,0];
function resetDefaults(){
var i=0;
for(i=1;i<=5;i++){
document.getElementById("value"+i).value=defaultValues[i-1];
document.getElementById("weight"+i).value=defaultWeights[i-1];
}
updateCalc();
}
function parseInput(id,minAllowed,isWeight){
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var val=parseFloat(el.value);
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function updateCalc(){
var values=[];
var weights=[];
var errors=false;
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var countValid=0;
var sumValues=0;
var i=0;
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var weightObj=parseInput("weight"+i,0,true);
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errors=true;
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values.push(valObj.value);
weights.push(weightObj.value);
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for(i=0;i0){
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sumWeighted+=values[i]*weights[i];
countValid+=1;
sumValues+=values[i];
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var mainResultEl=document.getElementById("mainResult");
var totalWeightsEl=document.getElementById("totalWeights");
var sumWeightedEl=document.getElementById("sumWeighted");
var simpleAvgEl=document.getElementById("simpleAvg");
var leadShareEl=document.getElementById("leadShare");
if(errors||sumWeights0?(sumValues/countValid).toFixed(2):"0.00″;
leadShareEl.textContent="0.00%";
renderTable(values,weights,sumWeights);
renderChart(values,weights);
return;
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var weightedAverage=sumWeighted/sumWeights;
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var leadShare=weights[0]>0?(weights[0]/sumWeights)*100:0;
leadShareEl.textContent=leadShare.toFixed(2)+"%";
renderTable(values,weights,sumWeights);
renderChart(values,weights);
}
function renderTable(values,weights,sumWeights){
var body=document.getElementById("tableBody");
body.innerHTML="";
var i=0;
for(i=0;i0?(weights[i]/sumWeights)*100:0;
tdNorm.textContent=norm.toFixed(2)+"%";
tr.appendChild(tdVal);
tr.appendChild(tdWei);
tr.appendChild(tdContrib);
tr.appendChild(tdNorm);
body.appendChild(tr);
}
}
function renderChart(values,weights){
var canvas=document.getElementById("waChart");
var ctx=canvas.getContext("2d");
var w=canvas.width;
var h=canvas.height;
ctx.clearRect(0,0,w,h);
var filteredValues=[];
var filteredWeights=[];
var i=0;
for(i=0;i0?filteredValues.length:1;
var maxVal=1;
for(i=0;imaxVal){
maxVal=Math.abs(filteredValues[i]);
}
if(Math.abs(contrib)>maxVal){
maxVal=Math.abs(contrib);
}
}
var padding=40;
var barWidth=(w-2*padding)/(bars*2.5);
var scale=(h-2*padding)/(maxVal===0?1:maxVal*1.2);
ctx.strokeStyle="#dbe3eb";
ctx.lineWidth=1;
ctx.beginPath();
ctx.moveTo(padding,h-padding);
ctx.lineTo(w-padding,h-padding);
ctx.lineTo(w-padding,padding);
ctx.stroke();
for(i=0;i<filteredValues.length;i++){
var x=padding+i*barWidth*2.5;
var valHeight=filteredValues[i]*scale;
ctx.fillStyle="#004a99";
ctx.fillRect(x,h-padding,barWidth,-valHeight);
var contrib=filteredValues[i]*filteredWeights[i];
var contribHeight=contrib*scale;
ctx.fillStyle="#28a745";
ctx.fillRect(x+barWidth*1.1,h-padding,barWidth,-contribHeight);
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ctx.fillStyle="#1e2a35";
ctx.font="12px Arial";
ctx.fillText("0",padding-12,h-padding+12);
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function copyResults(){
var main=document.getElementById("mainResult").textContent;
var tWeights=document.getElementById("totalWeights").textContent;
var sWeighted=document.getElementById("sumWeighted").textContent;
var sAvg=document.getElementById("simpleAvg").textContent;
var lead=document.getElementById("leadShare").textContent;
var text="Weighted average: "+main+"\nTotal weights: "+tWeights+"\nSum of weighted values: "+sWeighted+"\nSimple average: "+sAvg+"\nLead weight share: "+lead+"\nAssumption: weights emphasize importance.";
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resetDefaults();