What is a Bonding Curve?
A bonding curve is a mathematical formula that determines a token’s price based on its total supply. As more tokens are minted (bought), the price increases along the curve. As tokens are burned (sold), the price decreases. This creates a continuous, automated market without the need for order books or liquidity pools.
Bonding curves are the pricing engine behind many token launches, fair launch platforms, and social tokens.
How Bonding Curves Work
The most common bonding curve formula is:
Price = Supply² × Constant (or some other increasing function)
When a user buys tokens:
- They send ETH (or another reserve currency) to the contract
- The contract mints new tokens at the current curve price
- The price moves up along the curve
- The ETH is locked in the contract as the token’s reserve
When a user sells tokens:
- They send tokens to the contract
- The contract burns the tokens
- The contract sends back ETH from the reserve
- The price moves down along the curve
Every buyer has a guaranteed exit — the contract always has enough reserve to buy back tokens at the curve price.
Common Curve Shapes
| Curve Type | Price Behavior | Use Case |
|---|---|---|
| Linear | Price increases at a constant rate | Simple token launches |
| Exponential | Price increases faster as supply grows | Scarcity-driven tokens |
| Logarithmic | Price increases fast early, slows later | Fair distribution |
| S-curve (Sigmoid) | Slow → fast → slow | Phased token sales |
Real-World Examples
Pump.fun (Solana)
Pump.fun uses a bonding curve for memecoin launches. Tokens are minted along a fixed curve until a market cap threshold is reached, at which point liquidity is deposited to Raydium (a DEX) and the bonding curve is frozen.
Friend.tech (Base, now defunct)
Friend.tech used a bonding curve for “keys” (social tokens). As more people bought a creator’s key, the price increased exponentially — leading to speculation on social reputation.
UniV4 Hooks
Uniswap V4 hooks enable custom bonding curves for pools, allowing protocols to define their own pricing logic beyond constant product (x*y=k).
Risks and Criticisms
- Front-running: Since prices are deterministic, bots can front-run large buys
- Curve exhaustion: For exponential curves, late buyers face extreme prices with limited upside
- Rug risk: If the protocol controls the reserve, they can drain it — bonding curves don’t prevent exit scams
- Impermanent loss for curve operators: The contract bears the market-making risk
Bonding Curve vs AMM
| Aspect | Bonding Curve | AMM (x*y=k) |
|---|---|---|
| Price source | Mathematical formula from supply | Ratio of two tokens in pool |
| Token minting | Mints new tokens on buy | Swaps existing tokens |
| Liquidity | Protocol-owned (locked reserve) | LP-provided |
| Exit guarantee | Yes (contract always buys back) | Depends on pool liquidity |
Frequently Asked Questions
Q: Can you lose money on a bonding curve? A: Yes. If you buy tokens and other people sell before you, the curve price drops. Your tokens are worth less than what you paid — though you can always sell back to the curve.
Q: Is a bonding curve the same as an ICO? A: No. An ICO has a fixed price and fixed supply. A bonding curve has a dynamic price that changes with supply, and tokens can always be sold back to the contract.