Free TOPSIS Online — Multi-Criteria Decision Analysis

Need to compare multiple options across several criteria and reach an objective decision? TOPSIS is one of the world’s most widely used methods for exactly that — now available online, free, directly in your browser.

TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) was developed by Hwang and Yoon in 1981 and refined by Yoon in 1987. It is extensively used in engineering, supply chain management, finance, project management, healthcare, and academic research worldwide.

This tool implements the full TOPSIS algorithm with closeness coefficient CC, real-time sensitivity analysis, exportable HTML/PDF reports and JSON import/export — all in the browser, no login required.

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What is TOPSIS and how does it work

The core idea of TOPSIS is geometric: the best alternative is the one closest to the positive ideal solution (the best possible value on every criterion) and farthest from the negative ideal solution (the worst possible value).

The method follows 7 steps:

Step 1 — Decision matrix

Each alternative receives a score for each criterion. Scores can be on any scale — 1 to 10, real values, costs in dollars, percentages. TOPSIS normalises everything internally.

$x_{ij} = \text{score of alternative } i \text{ on criterion } j$

Step 2 — Vector normalisation

Values are normalised by dividing each score by the Euclidean norm of its column:

$r_{ij} = \frac{x_{ij}}{\sqrt{\sum_{k=1}^{m} x_{kj}^2}}$

This eliminates scale effects between criteria with different units (e.g. price in dollars and a 1–10 satisfaction rating become comparable).

Step 3 — Weighted normalised matrix

Each normalised value is multiplied by the criterion’s weight:

$v_{ij} = w_j \cdot r_{ij}$

Weights are automatically normalised to sum to 1, so you can use any scale (e.g. 1, 2, 3 or 10, 20, 30 — the result is equivalent).

Steps 4 & 5 — Ideal solutions

The positive ideal solution A⁺ is the vector with the best value for each criterion:

$A^+ = \left\{ v_j^+ \right\}, \quad v_j^+ = \begin{cases} \max_i v_{ij} & \text{if criterion } j \text{ is "higher is better"} \\ \min_i v_{ij} & \text{if criterion } j \text{ is "lower is better"} \end{cases}$

The negative ideal solution A⁻ is the vector with the worst value for each criterion (inverse logic).

Step 6 — Euclidean distances

For each alternative, compute the distance to the positive and negative ideal solutions:

$d_i^+ = \sqrt{\sum_{j=1}^{n} (v_{ij} - v_j^+)^2} \qquad d_i^- = \sqrt{\sum_{j=1}^{n} (v_{ij} - v_j^-)^2}$

Step 7 — Closeness coefficient (CC)

The closeness coefficient measures how close each alternative is to the ideal:

$CC_i = \frac{d_i^-}{d_i^+ + d_i^-} \in [0, 1]$

• CC = 1: alternative identical to the positive ideal solution
• CC = 0: alternative identical to the negative ideal solution
• The higher the CC, the better the alternative

The final ranking is sorted by CC in descending order.

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When to use TOPSIS

TOPSIS is ideal whenever you have multiple alternatives, multiple quantifiable criteria, and need an objective, justifiable result.

Personal decisions:

• Which car to buy considering price, fuel economy, comfort and maintenance
• Which smartphone or laptop offers the best value for money
• Buying vs renting vs financing a home
• Which job offer to accept (salary, growth, culture, location)
• Employee vs contractor — which working model suits your situation

Business decisions:

• Supplier selection based on price, quality, lead time and support
• Which software, tool or SaaS platform to adopt
• Which cloud provider to use (AWS, Google Cloud, Azure)
• Product feature prioritisation by impact, effort and revenue potential
• Bid evaluation in procurement processes

Career and education decisions:

• MBA, master’s, bootcamp or certification — which is worth more
• Which specialisation area to pursue
• Which startup or company to join as your next challenge

Finance and investment decisions:

• Comparing stocks, real estate funds, government bonds and CDs
• Which bank or fintech to use as your primary account
• Which health insurance plan to choose

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Criterion weights

The weight wⱼ represents the relative importance of each criterion. The tool automatically normalises weights to sum to 1.

A criterion with weight 4 has twice the influence of one with weight 2. The ratio between weights is what matters, not the absolute values.

How to set good weights:

• Distribute intuitively (e.g. price is 3× more important than aesthetics → weights 3 and 1)
• Use sensitivity analysis to check if the result changes with different weights
• If the decision is robust, the winner holds even with considerable weight variations

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Criterion direction

Each criterion can have one of two directions:

• ↑ Higher is better — use for revenue, score, satisfaction, quality
• ↓ Lower is better — use for cost, risk, time, defect rate

Direction is critical: if you mark “higher is better” for a cost criterion, TOPSIS will favour the most expensive alternative — the opposite of what you want.

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Sensitivity analysis

Sensitivity analysis answers: would the result change if I redistributed the weights?

Using the sliders you can identify:

• Whether the decision is robust — the winner holds even with large weight variations
• Which criterion has the most inversion power — enough to change the ranking if its weight increases
• Whether there is a dominant alternative (wins under any reasonable configuration) or if the result is sensitive to trade-offs

A robust decision is one where different priority profiles lead to the same winner. If the ranking shifts drastically with small weight changes, it signals conflicting criteria — and deeper analysis is warranted.

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TOPSIS vs. other multi-criteria methods

When to prefer TOPSIS:

• You have direct numeric scores (no need for pairwise comparisons)
• You want a fast, transparent, and auditable method
• You need to justify the decision to others with an objective coefficient

When to prefer PROMETHEE:

• You want to treat small differences as indifferent (preference function thresholds)
• You need to identify incomparable alternatives (PROMETHEE I)
• The criteria have non-linear preference structures

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Advantages and limitations of TOPSIS

Advantages:

• Scale-free — works with any unit ($, mph, %, 1–10 scores)
• Cardinal results — CC measures how good each alternative is, not just the ranking order
• Efficient — linear complexity, processes large matrices quickly
• Transparent — every step is auditable and explainable
• No pairwise interaction — does not require pairwise comparisons (unlike AHP)

Limitations:

• Scale sensitivity — criteria with very different magnitudes may dominate normalisation if not handled carefully
• No indifference zone — any difference, no matter how small, generates preference (unlike PROMETHEE with threshold functions)
• No incomparability — TOPSIS always produces a complete linear ranking

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How to use this tool

1. Select a ready-made scenario or click “Custom”
2. Configure alternatives (up to 8) and criteria (up to 8): name, weight and direction
3. Fill in the scores — use 1–10 scale, real values, or percentages. Use the same scale within each criterion
4. The ranking appears instantly with CC, d⁺ and d⁻ per alternative
5. Use the sliders to explore different weight configurations
6. Export the report as HTML or PDF, or save the analysis as JSON

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Ready-made scenarios available

Select directly in the tool one of the following pre-filled scenarios:

• 🚗 Choose a car — price, fuel economy, comfort and maintenance
• 💼 Job offer — salary, growth opportunities, company culture and location
• 💻 Laptop — price, performance, battery life and weight
• 🤝 Supplier — price, quality, lead time and support
• 💰 Investment — expected return, risk, liquidity and tax burden
• ☁️ Cloud provider — cost, services offered, support and ease of use
• 🛠️ Software tool — price, features, usability and support
• 🎓 MBA or certification — employability, cost, duration and flexibility
• 🏠 Buy or rent property — monthly cost, location, flexibility and wealth building
• 📱 Smartphone — price, camera, battery and performance
• 📝 Employee vs contractor — net income, stability, benefits and flexibility
• ⚛️ React, Vue or Angular — learning curve, ecosystem, performance and hiring market
• 🏦 Bank or fintech — fees, returns, customer service and app quality
• 🏥 Health insurance — monthly premium, coverage, network size and waiting periods
• 📋 Feature prioritisation — user impact, development effort and revenue potential
• ✈️ Travel destination — cost, weather, attractions and distance

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Decisions you can analyse with this tool

• free topsis online calculator multi-criteria decision
• how to use topsis method step by step example
• topsis multi-criteria decision analysis tool
• topsis supplier selection example
• best car multi-criteria analysis cost benefit
• compare job offers multiple criteria decision making
• best laptop value for money 2026 criteria comparison
• which smartphone to buy 2026 multi-criteria
• investment comparison risk return liquidity analysis
• buy rent or finance home multi-criteria decision
• employee vs contractor financial comparison analysis
• supplier selection topsis multi-criteria
• product feature prioritisation decision framework
• aws vs google cloud vs azure comparison criteria
• choose mba or bootcamp decision analysis
• free multi-criteria ranking tool topsis
• decision making multiple conflicting criteria weights
• topsis vs promethee vs ahp which method to use

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References

Hwang, C.L. & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer, Berlin.

Yoon, K.P. & Hwang, C.L. (1995). Multiple Attribute Decision Making: An Introduction. SAGE Publications.

Behzadian, M. et al. (2012). A state-of the-art survey of TOPSIS applications. Expert Systems with Applications, 39(17), 13051–13069.