Quadratic funding explained: formula, examples and limits

The quadratic funding formula

The formula takes three steps for each project:

1. Take the square root of each contribution.
2. Add the square roots together and square the sum. This is the project's ideal funding.
3. Subtract what donors gave. The difference is the project's ideal match, paid from the pool.

ideal funding = (√c1 + √c2 + ... + √cn)²
ideal match   = ideal funding − (c1 + c2 + ... + cn)

Here c1 to cn are the individual contributions to one project. Matching pools are usually smaller than the sum of all ideal matches, so each match is multiplied by the same scaling factor: the pool divided by the sum of all projects' ideal matches.

A worked example with two projects

The projects and amounts below are fictional, chosen so the square roots come out as whole numbers. Project A has 16 donors who give $25 each. Project B has 4 donors who give $100 each. Both raise $400, and the sponsor's matching pool is $3,600.

The ideal matches add up to $7,200, twice the size of the pool. The scaling factor is $3,600 ÷ $7,200 = 0.5, so each project gets half of its ideal match.

The matches add up to $3,000 + $600 = $3,600, exactly the pool. Both projects raised the same $400 from donors. Project A had four times as many donors and receives five times the match.

Now add a third case. A single donor gives $400 to Project C. The square root of 400 is 20, and 20² is $400, so Project C's ideal funding equals what it raised and its ideal match is $0.

Why many small donors beat one large one

Quadratic funding rewards breadth because of the square. If n donors each give the same amount c, the sum of square roots is n × √c, so the ideal funding is n² × c, which is n times what they gave. One donor gets back exactly their own gift and no match. Sixteen donors, as in Project A, get an ideal total of 16 times their donations before scaling.

The same logic shows up at the margin. If a 17th donor gives $1 to Project A, the sum of square roots rises from 80 to 81. The ideal funding becomes 81² = $6,561, and the ideal match becomes $6,561 − $401 = $6,160, up $160. If instead one of the existing donors adds $1 (from $25 to $26), the ideal match rises by about $15. Before scaling, a new supporter is worth roughly ten times as much as a bigger gift from an old one. Scaling changes the amounts, not the direction.

How the match is scaled to the pool

Scaling every match by one factor is the budget-limited version the paper itself proposes. The authors call it capital-constrained quadratic finance (CQF): "an α mixture of QF with a 1 − α weight on un-matched private contributions." In plain terms, each project receives α × (its ideal funding) + (1 − α) × (its donations), and the sponsor sets α low enough to stay within the budget.

With α = 0.5, Project A receives 0.5 × $6,400 + 0.5 × $400 = $3,400, and Project B receives 0.5 × $1,600 + 0.5 × $400 = $1,000. Those are the same totals as in the table above. Scaling the matches by 0.5 and setting α to 0.5 are the same operation.

Real rounds add rules on top, such as the per-project cap Gitcoin used in GG24.

Sybil attacks, collusion and identity checks

Quadratic funding's weak point is that it pays for headcount, and headcount is cheap to fake with crypto wallets. A sybil attack is one person posing as many. In the example above, $400 from one wallet earns no match. The same $400 split across 16 wallets of $25 each has an ideal match of $6,000.

The paper is direct about it: "The simplest and most clearly necessary solution to fraud is an effective system of identity verification." It calls collusion, such as groups trading donations or paying donors back, "perhaps the greatest challenge for QF".

The quadratic funding programs in our directory use these defenses:

• Gitcoin Grants: in GG24, donors had to pass Human Passport checks for their donations to be matched, and matching used Connection-Oriented Cluster Match (COCM).
• Giveth QF rounds: matching uses COCM to limit sybil attacks, payouts follow a 2 to 3 week fraud review, and projects lose matching for quid-pro-quo incentives, fake donors, recirculated funds or misusing funds.
• Octant: votes are verified on-chain with zero-knowledge proofs, and accepted projects complete KYC or KYB before the round.

COCM is a QF variant that gives less matching weight to groups of donors who appear closely connected than to the same number of independent donors.

The limits of quadratic funding

Quadratic funding measures how many people back a project, which is not the same as how useful the project is. Its main limits:

• It rewards reach. Projects with large communities do well; deep infrastructure with few direct users can be underfunded even when many projects depend on it.
• Identity checks cost something. Real donors who can't or won't pass them go unmatched.
• The pool is set by a sponsor. Your match depends on its size and on how many projects compete for it.
• Income is unpredictable. You don't know your match until the round closes, and rounds can stop. Gitcoin has not run one since October 2025.
• Collusion is hard to rule out. Fraud reviews catch some of it; the paper's authors treat it as an open problem.

Where quadratic funding runs as of October 2026

All three quadratic funding programs in web3grant's directory are between rounds as of October 31, 2026.

• Gitcoin GrantsGitcoinNo round since GG24 in October 2025, and none is announced. As of October 2026 Gitcoin is folding quadratic funding into a local-money pilot targeted for November, with a wider launch in mid-December; there is no application for builders yet.Up to $10.9KClosed
• Giveth QF roundsGivethApplications for the Stellar round closed on Aug 28. Donations run until Oct 4, 2026, and no next round is announced.Up to $86KClosed
• Octant funding epochsOctantEpoch 13 applications have closed. Community allocation for its 100 ETH pool runs Oct 14 to Oct 21, 2026, and Epoch 14 has no date yet.$500–$27.6KClosed

Gitcoin Grants

Gitcoin Grants ran rounds from 2019 in which community donations were matched from a shared pool, mostly with quadratic funding; Gitcoin says more than $60M went out. GG24, in October 2025, allocated about $1.8M across six domains, each with its own operator and mechanism, only some of them quadratic.

No round has run since, and none is announced. As of October 2026, Gitcoin is folding quadratic funding into a "local money" pilot targeted for November, with a wider launch in mid-December, aimed at local public goods such as jobs, mutual aid and physical space. There is no application for builders yet. See how Gitcoin Grants works for the details.

Giveth QF rounds

Giveth is a donation platform where any project can list and receive donations at any time. Several times a year it runs quadratic funding rounds with a partner who funds the matching pool and helps set eligibility. TheDAO's Ethereum Security round (April 23 to May 14, 2026) matched 134 projects from a pool of over 637 ETH. The Stellar Community Growth round, with a $50,000 matching pool, closed applications on August 28 and donations on October 4, 2026. No next round is announced. Payouts are in ETH, USDC or XLM.

Octant

Octant, a Golem Foundation project, runs funding rounds called epochs. Selected projects are listed, community members allocate funds to them, and a matching pool is split using quadratic funding. Since Octant v2 in 2026, contributors can allocate rewards earned by locking GLM or put in WETH from their wallet. Epoch 12 paid 88.1 WETH to 25 projects. Epoch 13, the Privacy Round, had a 100 ETH matching pool and its community allocation ran in mid-October 2026; Epoch 14 has no date yet.

How to prepare for a quadratic funding round

The preparation that matters is mostly done before the round opens:

• Count donors, not dollars. Fifty people giving $5 move the match far more than one person giving $250.
• Check the donor rules early. If donors must pass an identity check, as with Human Passport in GG24, tell your supporters before the window opens.
• Offer nothing in return for donations. Giveth removes matching for quid-pro-quo incentives, and other rounds screen for the same thing.
• Build the community first. A short donation window rewards supporters you already have.
• Treat the match as a bonus. Plan your runway on other sources, as covered in our guide to sustainable funding for open source crypto projects.

To hear when a matching round opens, use the deadline calendar or sign up for deadline alerts. If your work already has a track record, retroactive public goods funding is the other community-funding model to know.

FAQ

Who invented quadratic funding?

Quadratic funding was proposed by Vitalik Buterin, Zoë Hitzig and E. Glen Weyl in the paper "A Flexible Design for Funding Public Goods", first posted to arXiv in September 2018. The paper extends ideas from quadratic voting to funding and sets out the rule that a project receives the square of the sum of the square roots of its contributions. Gitcoin Grants later became its best-known use in Web3.

Is quadratic funding the same as quadratic voting?

Quadratic funding is not the same as quadratic voting, though the two are related. In quadratic voting, casting more votes on one issue costs quadratically more, so people spread influence across issues they care about. Quadratic funding applies a similar square-root logic to money: each contribution counts by its square root, then the sum is squared, so broad support earns more matching than concentrated support.

What happens when the matching pool is too small?

When the matching pool is smaller than the sum of all ideal matches, which is the normal case, each project's ideal match is multiplied by the same factor: the pool divided by the total of ideal matches. The paper's capital-constrained version does the same thing with a parameter called alpha. Rounds may also cap how much any single project can receive.

Can I donate to my own project in a quadratic funding round?

Rules on self-donation vary by round, but self-dealing is exactly what quadratic funding rounds screen for. Giveth, for example, removes matching from projects with fake donors, recirculated funds or quid-pro-quo incentives, and payouts wait for a fraud review. Read the round's eligibility rules before anyone on your team donates, and never route money back to donors.