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What is quadratic funding? The 4×€1 vs 1×€4 example

27 October 2026 · 4 min

Quadratic funding gives more matching to initiatives with many small donors than to those with one large donor. A worked example.

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Quadratic funding is the model in the name of AQFILYI. Together with young people in Montenegro, we are working out how it can fund local initiatives. This article explains how the formula works.

Quadratic funding (QF) is a way to share out a matching pool. An initiative that many people support with small amounts receives more matching than one that a few people support with large amounts. The formula is:

funding = (√c₁ + √c₂ + … + √cₙ)²

Each c is the total that one person gave to one initiative.

The example

Assume the matching pool is large enough to cover every request.

Scenario A: four people give €1 each

  • Total donations: €4
  • Sum of square roots: √1 + √1 + √1 + √1 = 1 + 1 + 1 + 1 = 4
  • Funding after the formula: 4² = €16
  • Matching added: €16 − €4 = €12

Scenario B: one person gives €4

  • Total donations: €4
  • Sum of square roots: √4 = 2
  • Funding after the formula: 2² = €4
  • Matching added: €4 − €4 = €0

Both initiatives raised €4. Initiative A receives €12 in matching because four different people supported it. Initiative B receives nothing extra, because all of its support came from one person.

What the example shows

The formula gives weight to the number of supporters as well as to the amount. An initiative that 100 people support receives more matching than one that a single person supports, even when the totals are the same.

When the pool is smaller than the requests

In practice the matching pool is limited. When the requests add up to more than the pool, each initiative's match is reduced in proportion:

actualMatch = requestedMatch × (poolSize / sumOfAllRequestedMatches)

The pool therefore never pays out more than it holds.

Fake accounts

Quadratic funding can be gamed: one person creates many accounts and gives a small amount from each, so that one supporter looks like many. This is called a Sybil attack. Any QF system needs a way to check that each supporter is a separate person.

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