How to use the topsis multi-criteria ranking calculator
- List the criteria, one per line: name, weight and whether it is a benefit (higher is better) or a cost (lower is better).
- List the options, one per line: name followed by one value for each criterion in the same order.
- Read the ranking by closeness to the ideal solution, with the distance to the best and to the worst.
- Check the criteria table for the weight shares and the best and worst value in each column.
Formula
Scaled value = value / square root of the sum of squares of its column
Weighted value = scaled value x (weight / sum of weights)
Best point: highest weighted value for benefits, lowest for costs; worst point is the opposite
Closeness = distance to the worst / (distance to the best + distance to the worst)
Distances are ordinary Euclidean distances across all criteria. Closeness runs from 0 to 1, and the highest value ranks first.
Choosing a laptop
Four laptops are compared on price (cost, weight 4), battery hours (benefit, 3), weight in kg (cost, 2) and a review score (benefit, 3). The weight shares are 33.3%, 25.0%, 16.7% and 25.0%.
Laptop A is closest to the ideal with 0.5690, followed by Laptop C (0.5178), Laptop B (0.5053) and Laptop D (0.4817). The cheapest laptop does not rank first because its battery and score pull it away from the ideal.
The idea behind TOPSIS
TOPSIS stands for technique for order preference by similarity to ideal solution. It imagines a perfect option that takes the best value in every criterion and a worst option that takes the worst, and then ranks real options by how near they are to the perfect one and how far from the worst. An option that is only average everywhere can rank above one that is excellent in one place and poor in another.
Scaling each column by its length makes criteria in different units comparable, so price in dollars and weight in kilograms can sit in one calculation. The weights then say how much each matters.
What to watch for
The weights are your judgment, and the ranking can change when they do. Try a few sets to see whether the top option is stable. TOPSIS also ranks options only against each other, so adding a new option changes the scaling and can reorder the rest, a known property of the method.
It differs from a weighted sum, which adds up weighted scores, and from AHP, which builds weights from pairwise comparisons. Use it as a structured way to compare options, and check the result against common sense before you decide.
Assumptions and limits
- Values are numbers of 0 or more, and every option has a value for every criterion.
- Each criterion is either a benefit or a cost, and weights are above 0.
- Ties get the same rank. Up to 10 criteria and 30 options are read.
- The figures are examples. Nothing is uploaded.
Frequently asked questions
Do the weights have to add up to 1?
No. Enter any positive numbers. The page divides each by the total to get the weight share.
What if a criterion has all zeros?
It cannot be scaled, because its column length is 0. Remove it or enter real values.
Can I use negative values?
Not in this version. Shift the scale so values are 0 or more.
Why does the ranking change when I add an option?
The scaling and the best and worst points depend on all the options in the table, so a new option can move them.