TOPSIS Calculator
The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision analysis method.
TOPSIS is based on the concept that the chosen alternative should have the shortest geometric distance from the best ideal solution and the longest from the worst ideal solution.
New here? Try it with example data
Fill every step with “Choosing a laptop” and see a result in one click.
Enter at least three alternatives
Insert criteria
| No. | Name | Type | Weight | Qualitative | Actions |
|---|---|---|---|---|---|
| 1 | Benefit | ||||
| 2 | Benefit |
Complete previous steps
Complete previous steps
How TOPSIS works
TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) ranks alternatives by their geometric distance to an ideal solution that is best on every criterion and to an anti-ideal solution that is worst on every criterion.
Step by step
- Rescale the criteria weights so they sum to 1.
- Normalize each criterion column of the performance matrix by dividing every value by the length of that column (vector normalization), so that euros, hours and kilograms become comparable.
- Multiply the normalized values by the criterion weights.
- Build the ideal solution (largest weighted value for benefit criteria, smallest for cost criteria) and the anti-ideal solution (the opposite).
- Measure each alternative's Euclidean distance to the ideal solution and to the anti-ideal solution.
- Compute the closeness score: the distance to the anti-ideal divided by the sum of both distances. Rank alternatives from the highest score to the lowest.
Formulas
Worked example
With the laptop data above (Price and Weight are cost criteria, Performance and Battery are benefit criteria), the calculator returns these distances and closeness scores.
| Alternative | Price (EUR) (cost, weight 3) | Performance score (benefit, weight 3) | Battery (hours) (benefit, weight 2) | Weight (kg) (cost, weight 2) |
|---|---|---|---|---|
| Brisk 15 | 900 | 6 | 9 | 1.8 |
| Cirrus Pro | 1500 | 9 | 10 | 1.6 |
| Aurora 14 | 1200 | 8 | 12 | 1.3 |
| Delta Air | 1050 | 7 | 15 | 1.2 |
| Alternative | Distance to ideal | Distance to anti-ideal | Closeness | Rank |
|---|---|---|---|---|
| Brisk 15 | 0.088 | 0.076 | 0.463 | 3 |
| Cirrus Pro | 0.091 | 0.061 | 0.402 | 4 |
| Aurora 14 | 0.050 | 0.069 | 0.579 | 2 |
| Delta Air | 0.044 | 0.089 | 0.669 | 1 |
Delta Air is closest to the ideal laptop (closeness 0.669) even though it is neither the cheapest nor the fastest: it is consistently good on all four criteria. Cirrus Pro has the best performance but is the most expensive, which pushes it to last place.
Use the "Load example" button at the top of this page to fill in this data and run it yourself.
Frequently asked questions
What does the TOPSIS closeness score mean?
It is a number between 0 and 1. A score of 1 would mean an alternative equals the ideal solution on every criterion, and 0 would mean it equals the anti-ideal solution. Higher is better, and the ranking is simply the scores sorted from high to low.
How do I choose the criteria weights?
Weights are relative importance: enter any positive numbers and the calculator rescales them so they sum to 1. Weights of 3, 3, 2 and 2 are the same as 30%, 30%, 20% and 20%. If you find it hard to weigh criteria directly, compare them in pairs with the AHP consistency checker and use its priority vector as your weights.
How does TOPSIS treat cost criteria like price?
Set the criterion Type to Cost. For a cost criterion the ideal value is the smallest weighted value rather than the largest, so cheaper or lighter alternatives get closer to the ideal.
How is TOPSIS different from SAW?
SAW adds up weighted scores, so a strong result on one criterion can offset a weak one on another. TOPSIS measures distance to an ideal point and an anti-ideal point, so the two methods can rank alternatives differently.
How many alternatives and criteria can I use?
You need 3 to 7 alternatives and 2 to 7 criteria, and every performance value must be greater than zero.