This weighted geometric mean calculator lets you input values and weights, see the weighted geometric mean instantly, and explore intermediate math steps so you can trust the calculation.
Weighted Geometric Mean Calculator Inputs
Enter positive numbers only. Example: 3, 5, 9, 4
Weights must be positive and align one-to-one with values.
Choose rounding precision between 0 and 10.
Weighted Geometric Mean: —
Sum of Weights: —
Weighted Log Average: —
Normalized Weights: —
Geometric Mean Without Weights: —
Weighted Components Table
#
Value
Weight
Normalized Weight
Weight × ln(Value)
Blue bars: values | Green bars: weights (scaled)
The weighted geometric mean formula multiplies each value raised to its weight power, which is equivalent to exponentiating the weighted average of natural logarithms. This weighted geometric mean calculator shows each step so you can verify the math.
What is a Weighted Geometric Mean Calculator?
A weighted geometric mean calculator is a precision tool that computes the geometric average when each data point carries its own importance. The weighted geometric mean calculator is essential for portfolio growth rates, multi-period risk assessments, and any multiplicative process where different factors matter unequally. Professionals use a weighted geometric mean calculator to compare investment baskets, harmonize index constituents, and normalize performance ratios. A common misconception is that a weighted geometric mean calculator behaves like an arithmetic average; in reality the weighted geometric mean calculator captures compounding effects and proportional influence.
Analysts, CFOs, quants, and risk managers rely on a weighted geometric mean calculator whenever outcomes multiply across periods or factors. Unlike a simple average, a weighted geometric mean calculator penalizes outliers that could distort compounding. This weighted geometric mean calculator page ensures every user understands how the math respects proportional weights and the requirement that all values remain positive.
Internal resource: {related_keywords} provides deeper context on compounding analysis for anyone expanding their toolkit with this weighted geometric mean calculator.
Weighted Geometric Mean Calculator Formula and Mathematical Explanation
The weighted geometric mean calculator uses the formula:
G = exp( Σ (wi × ln(xi)) / Σ wi ). In words, the weighted geometric mean calculator takes the natural log of each positive value xi, multiplies by its weight wi, sums the results, divides by the total weight, then exponentiates. This weighted geometric mean calculator approach equals multiplying each value raised to its normalized weight power, which preserves proportional influence.
Derivation steps are shown in the calculator output: sum of weights, weighted log average, and exponentiation. Each variable must stay positive because logarithms of negative numbers are undefined, and the weighted geometric mean calculator enforces that safeguard.
Variables in the Weighted Geometric Mean Calculator
Variable
Meaning
Unit
Typical Range
xi
Positive data value
Same as dataset
Greater than 0
wi
Weight of value i
Unitless
0 to 1 (or scaled)
Σw
Sum of all weights
Unitless
0.1 to 100
ln(x)
Natural logarithm of value
Unitless
Depends on x
G
Weighted geometric mean result
Same as dataset
Greater than 0
For more discussion on log-based averaging, review {related_keywords} inside this weighted geometric mean calculator guide.
Practical Examples (Real-World Use Cases)
Example 1: An investment analyst uses the weighted geometric mean calculator for four quarterly growth multipliers: 1.04, 0.97, 1.06, 1.02 with weights 0.25, 0.25, 0.35, 0.15 to reflect capital allocation. The weighted geometric mean calculator outputs a compounded growth factor near 1.022, meaning roughly 2.2% growth after adjusting for allocation.
Example 2: A product team evaluates reliability factors: uptime ratios 0.999, 0.995, 0.997 with weights 0.5, 0.3, 0.2. The weighted geometric mean calculator delivers an overall reliability factor of about 0.9975, which guides SLA commitments. These realistic examples show how the weighted geometric mean calculator respects multiplicative behaviors.
See {related_keywords} for additional portfolio cases that complement this weighted geometric mean calculator.
How to Use This Weighted Geometric Mean Calculator
Enter all positive values into the weighted geometric mean calculator as a comma-separated list.
Add matching weights; the weighted geometric mean calculator checks alignment and positivity.
Set decimal places for rounding and watch real-time updates.
Review sum of weights, normalized weights, and weighted log average before trusting the result.
Use Copy Results to paste the weighted geometric mean calculator output into reports.
The weighted geometric mean calculator results panel highlights the primary mean, shows intermediate math, and confirms whether weights sum to meaningful totals. A detailed legend under the chart clarifies values versus weight scaling.
For additional guidance, explore {related_keywords} alongside this weighted geometric mean calculator.
Key Factors That Affect Weighted Geometric Mean Results
The weighted geometric mean calculator reveals how several factors shift outcomes:
Weight concentration: Larger weights on small values pull the weighted geometric mean lower.
Value volatility: Extreme multiplicative swings impact the weighted geometric mean calculator more than linear averages.
Weight normalization: Scaling weights changes influence even if the sum differs, handled automatically by the weighted geometric mean calculator.
Time sequencing: Compounding across periods benefits from this weighted geometric mean calculator because order is multiplicative.
Risk and downside floors: The weighted geometric mean calculator is sensitive to values near zero, highlighting risk controls.
Fees, taxes, and drags: Adjusted values fed into the weighted geometric mean calculator reflect net performance.
Need portfolio-specific guidance? Visit {related_keywords} while using this weighted geometric mean calculator.
Frequently Asked Questions (FAQ)
Why must values be positive? The weighted geometric mean calculator uses natural logs, which require positive inputs.
Can weights be percentages? Yes, the weighted geometric mean calculator normalizes any positive weights.
What if weights do not sum to 1? The weighted geometric mean calculator divides by the sum, so scaling is automatic.
Is the result sensitive to a single low value? Yes, a small value with a large weight can drastically lower the weighted geometric mean calculator output.
How is this different from arithmetic mean? The weighted geometric mean calculator handles multiplicative effects, not additive.
Can I include zero? No, zero makes the log undefined; the weighted geometric mean calculator will flag it.
Does order matter? No, the weighted geometric mean calculator depends on sets, not sequence.
How many items can I enter? The weighted geometric mean calculator is built for multiple comma-separated pairs; practical limits depend on readability.
Related Tools and Internal Resources
Expand your toolkit beyond this weighted geometric mean calculator with these resources:
{related_keywords} – Deep dive on compounded return analysis linked to this weighted geometric mean calculator.
{related_keywords} – Guide to portfolio weighting strategies compatible with the weighted geometric mean calculator.
{related_keywords} – Risk-adjusted performance metrics to pair with the weighted geometric mean calculator.
{related_keywords} – Inflation and fee adjustments before using the weighted geometric mean calculator.
{related_keywords} – Data cleaning checklist for accurate weighted geometric mean calculator inputs.
{related_keywords} – Reporting templates that integrate the weighted geometric mean calculator output.
var defaultValues = "3, 5, 9, 4";
var defaultWeights = "0.2, 0.3, 0.4, 0.1";
var defaultPrecision = 4;
function resetCalculator(){
document.getElementById("valuesInput").value = defaultValues;
document.getElementById("weightsInput").value = defaultWeights;
document.getElementById("precisionInput").value = defaultPrecision;
clearErrors();
calculateWeightedGM();
}
function clearErrors(){
document.getElementById("valuesError").textContent = "";
document.getElementById("weightsError").textContent = "";
document.getElementById("precisionError").textContent = "";
}
function parseList(str){
var parts = str.split(",");
var arr = [];
for(var i=0;i10){
document.getElementById("precisionError").textContent = "Precision must be between 0 and 10.";
valid = false;
}
var values = parseList(valuesStr);
var weights = parseList(weightsStr);
if(valuesStr.trim()===""){
document.getElementById("valuesError").textContent = "Enter at least one value.";
valid = false;
}
if(weightsStr.trim()===""){
document.getElementById("weightsError").textContent = "Enter matching weights.";
valid = false;
}
if(values.length!==weights.length){
document.getElementById("weightsError").textContent = "Values and weights must have the same count.";
valid = false;
}
for(var i=0;i<values.length;i++){
if(!validNumber(values[i]) || values[i]<=0){
document.getElementById("valuesError").textContent = "All values must be positive numbers.";
valid = false;
break;
}
}
for(var j=0;j<weights.length;j++){
if(!validNumber(weights[j]) || weights[j]<=0){
document.getElementById("weightsError").textContent = "All weights must be positive numbers.";
valid = false;
break;
}
}
if(!valid){
updateDisplay("–","–","–","–");
clearTable();
clearChart();
return;
}
var sumWeights = 0;
for(var k=0;k<weights.length;k++){ sumWeights += weights[k]; }
var weightedLogSum = 0;
for(var m=0;m<values.length;m++){
weightedLogSum += weights[m]*Math.log(values[m]);
}
var weightedLogAverage = weightedLogSum / sumWeights;
var geometricMean = Math.exp(weightedLogAverage);
var unweightedSumLogs = 0;
for(var n=0;n<values.length;n++){ unweightedSumLogs += Math.log(values[n]); }
var unweightedGM = Math.exp(unweightedSumLogs/values.length);
var normWeightsArr = [];
for(var p=0;p<weights.length;p++){
normWeightsArr.push(weights[p]/sumWeights);
}
updateDisplay(geometricMean.toFixed(precision), sumWeights.toFixed(precision), weightedLogAverage.toFixed(precision), unweightedGM.toFixed(precision), normWeightsArr);
buildTable(values, weights, normWeightsArr, precision);
drawChart(values, weights);
}
function updateDisplay(mainResult, sumWeights, weightedLogAvg, unweightedGM, normWeightsArr){
document.getElementById("resultMain").textContent = "Weighted Geometric Mean: " + mainResult;
document.getElementById("sumWeights").textContent = sumWeights;
document.getElementById("weightedLogAverage").textContent = weightedLogAvg;
document.getElementById("unweightedGM").textContent = unweightedGM;
if(normWeightsArr){
var text = "";
for(var i=0;i0?", ":"") + normWeightsArr[i].toFixed(4);
}
document.getElementById("normalizedWeights").textContent = text;
} else {
document.getElementById("normalizedWeights").textContent = "–";
}
}
function clearTable(){
document.getElementById("dataTableBody").innerHTML = "";
}
function buildTable(values, weights, normWeightsArr, precision){
var tbody = document.getElementById("dataTableBody");
var html = "";
for(var i=0;i<values.length;i++){
var weightedLn = (weights[i]*Math.log(values[i])).toFixed(precision);
html += "
"+(i+1)+"
"+values[i]+"
"+weights[i]+"
"+normWeightsArr[i].toFixed(4)+"
"+weightedLn+"
";
}
tbody.innerHTML = html;
}
function clearChart(){
var canvas = document.getElementById("chartCanvas");
var ctx = canvas.getContext("2d");
ctx.clearRect(0,0,canvas.width,canvas.height);
}
function drawChart(values, weights){
var canvas = document.getElementById("chartCanvas");
var ctx = canvas.getContext("2d");
ctx.clearRect(0,0,canvas.width,canvas.height);
var padding = 40;
var width = canvas.width – padding*2;
var height = canvas.height – padding*2;
var maxVal = 0;
for(var i=0;imaxVal){ maxVal = values[i]; }
}
var maxWeight = 0;
for(var j=0;jmaxWeight){ maxWeight = weights[j]; }
}
var scaleWeight = maxWeight>0 ? maxVal/maxWeight/1.2 : 1;
var barWidth = width/(values.length*3);
ctx.strokeStyle = "#cfd6de";
ctx.lineWidth = 1;
ctx.beginPath();
ctx.moveTo(padding, padding);
ctx.lineTo(padding, padding+height);
ctx.lineTo(padding+width, padding+height);
ctx.stroke();
for(var idx=0; idx<values.length; idx++){
var xBase = padding + idx*barWidth*3 + barWidth*0.2;
var valHeight = (values[idx]/(maxVal*1.1))*height;
ctx.fillStyle = "#004a99";
ctx.fillRect(xBase, padding+height – valHeight, barWidth, valHeight);
var weightHeight = (weights[idx]*scaleWeight/(maxVal*1.1))*height;
ctx.fillStyle = "#28a745";
ctx.fillRect(xBase+barWidth+4, padding+height – weightHeight, barWidth, weightHeight);
ctx.fillStyle = "#6c757d";
ctx.font = "12px Arial";
ctx.fillText("V"+(idx+1), xBase, padding+height + 14);
}
ctx.fillStyle = "#004a99";
ctx.fillText("Values", padding + 10, padding – 10);
ctx.fillStyle = "#28a745";
ctx.fillText("Weights (scaled)", padding + 80, padding – 10);
}
function copyResults(){
var main = document.getElementById("resultMain").textContent;
var sumW = document.getElementById("sumWeights").textContent;
var wLog = document.getElementById("weightedLogAverage").textContent;
var norm = document.getElementById("normalizedWeights").textContent;
var unweighted = document.getElementById("unweightedGM").textContent;
var text = main + "\nSum of Weights: " + sumW + "\nWeighted Log Average: " + wLog + "\nNormalized Weights: " + norm + "\nUnweighted Geometric Mean: " + unweighted + "\nAssumption: all values and weights are positive.";
if(navigator.clipboard && navigator.clipboard.writeText){
navigator.clipboard.writeText(text);
}
}
calculateWeightedGM();