Bonding curves are mathematical pricing models used in the crypto world to determine token prices based on their supply. They’re vital in DAOs, token launches, prediction markets, and GameFi projects, helping automate pricing and liquidity without intermediaries.

What is a Bonding Curve?

In simple terms, a bonding curve adjusts the price of a token as its supply changes. The more tokens are minted (bought), the higher the price becomes. When tokens are burned (sold), the price drops. This relationship is governed by a reserve (like ETH or DAI), which ensures liquidity.

Types of Bonding Curves

1. Linear Bonding Curve

Follows the equation: P(s) = a * s + b

• Predictable price increases as supply grows.

• Good for DAO fundraising and fair token distribution.

2. Exponential Bonding Curve

Follows: P(s) = a * (1 + r)^s

• Prices grow rapidly, rewarding early adopters.

• Ideal for NFT launches and scarce token sales.

3. Logarithmic Bonding Curve

Uses: P(s) = a * ln(s + 1)

• Prices rise fast at first, then slow down.

• Best for governance tokens with wide adoption goals.

4. Sigmoid (S-Curve)

Follows: P(s) = L / (1 + e ^ (-k * (s - x0)))

• Price starts low, spikes in the middle, and flattens.

• Suitable for reputation systems and social tokens.

Key Use Cases

• Fundraising: Fair token issuance based on demand.

• DeFi Protocols: Automated pricing in AMMs.

• Governance Tokens: Balanced and incentivized access.

• Stablecoins: Price adjustments through supply control.

Common Attack Vectors

Despite their utility, bonding curves are prone to certain vulnerabilities:

• Front-running: Attackers profit by manipulating transaction order.

• Flash Loans: Temporary price distortion for malicious gains.

• Arithmetic Bugs: Misuse of math functions can cause underflows/overflows.

• Oracle Manipulation: Influencing external data to affect pricing.

Mitigations include using secure math libraries, enforcing transaction limits, and applying anti-MEV protections.

👉 Wanna go deeper?*
We’ve covered bonding curve types, use cases, smart contract logic and attack vectors in our full blog:
*🔗 A Guide to Bonding Curves (Types & Auditing Methodology)

Security Best Practices

When implementing bonding curves in smart contracts:

• Always use tested math libraries like PRBMath or ABDKMath64x64.

• Implement circuit breakers, tax limits, and input validations.

• Audit for rounding errors, zero-value logic flaws, and edge-case behaviors.

At QuillAudits, we specialize in securing smart contracts with complex logic like bonding curves. Our multi-layered auditing framework has protected over $3B in digital assets.