Weighted Average Calculator: Length Weighted Grades and Costs
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Weighted Average Calculator
A weighted mean with the plain mean shown beside it, because the gap between the two is the whole point. Weights can be lengths, hours, masses, credit units or anything else that measures how much each value counts.
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The weighted mean is the sum of value times weight, divided by the sum of weights. The classic field example: a 1 m sample at 2.1 g/t next to a 9 m sample at 0.4 g/t averages 0.57 g/t once length weighted. The plain mean of 1.25 would overstate the grade by more than double.
How to use this tool
Enter each value with its weight, add rows as needed, and the tool returns the weighted mean with the plain mean beside it. The weight column is whatever measures how much each value should count: sample length, hours worked, mass, credit units, number of tests.
It opens loaded with a deliberately awkward example: a 1 m sample at 2.1 next to a 9 m sample at 0.4. The weighted mean is 0.57. The plain mean is 1.25. Which one is right depends entirely on the question, and the gap between them is why this tool shows both.
What weighting actually does
The weighted mean is the sum of each value times its weight, divided by the sum of the weights. When all weights are equal it collapses to the ordinary mean, which is a useful way to see the plain mean for what it is: a weighted mean that quietly assumes every value counts the same.
That assumption fails whenever the values represent unequal amounts of something. Averaging assay grades from intervals of different lengths, unit costs from orders of different sizes, or speeds over legs of different durations all need the weighting, because in each case the short interval, the small order and the quick leg genuinely matter less.
The field example, in full
Drillhole samples: 1 m at 2.1 g/t and 9 m at 0.4 g/t. The weighted calculation is 1 times 2.1 plus 9 times 0.4, which is 2.1 plus 3.6, giving 5.7 gram metres over 10 m of core, so 0.57 g/t. The plain mean of 2.1 and 0.4 is 1.25, more than double, and it is wrong for grade because it lets one metre of rock speak with the same voice as nine.
This is exactly the length weighting that resource estimation calls compositing, and the reason a high grade sliver never dominates a composite the way it dominates a naive average.
A worked check you can repeat on paper
Three concrete pours: 12 cubic metres at 285 per cube, 30 at 265, and 8 at 310. The weighted unit cost is 12 times 285 plus 30 times 265 plus 8 times 310, which is 3420 plus 7950 plus 2480, giving 13850 over 50 cubes, so 277 per cube. The plain mean of the three rates is 286.67, nearly 10 higher, because it ignores that the cheap rate covered most of the volume.
Mistakes that catch people out
Averaging averages. The mean of two site averages is not the site wide average unless both sites contributed equally. Fix: weight each average by its count.
Averaging speeds by trip instead of by time. An hour at 40 and an hour at 60 averages 50, but equal distances at 40 and 60 average 48, because the slow leg takes longer. Fix: weight speeds by time.
Letting zero weight rows vanish silently. A row with weight zero contributes nothing, which is sometimes intended and sometimes a typo. Fix: check the sum of weights the tool reports against what you expect.
Weighting by the wrong column. Grades weight by length or mass, costs weight by quantity, speeds weight by time. Fix: the weight is always the thing the value is per.
How this was checked
The calculation was verified against hand worked values: three rows of 1.5, 3.0 and 2.0 with weights 2, 4 and 1 returning 17 sevenths, the drillhole pair returning exactly 0.57, and a degenerate case of identical values under wildly different weights returning the value unchanged, which any correct weighting must. The plain mean is computed independently rather than derived, so the comparison between the two is honest.
Related Calculators and Reference
See also the Mean, Median and Mode Calculator for the unweighted versions, plus the median and mode that a weighted average cannot give you. For grades weighted by credits on the 4.0 scale, the GPA Calculator does the whole sum. Also see the Final Grade Calculator: the score needed on the final when the other categories are already graded.
The full drillhole version, with composite boundaries and multiple holes, is the Drillhole Assay Compositing Tool. Interval velocities combine by the same principle in the Seismic Velocity Converter, where the Dix equation is time weighted averaging wearing different clothes. Percentage weightings connect to the Percentage Calculator, and grade tonnage consequences of compositing appear in the Grade Tonnage Curve Calculator.