The Math Behind Bonding Curves

What is a Bonding Curve?

A bonding curve is a mathematical function that determines token price based on supply. More tokens sold = higher price. This creates automatic price discovery without order books.

The Formula

Spawned uses a linear bonding curve:

Price = BasePrice + (Slope × CurrentSupply)

Where:

• BasePrice: Starting price (very low)
• Slope: Rate of price increase
• CurrentSupply: Tokens already sold

Practical Example

Settings:

• Base price: 0.000001 SOL
• Slope: 0.00000001 per token
• Current supply: 100,000,000 tokens sold

Current price: 0.000001 + (0.00000001 × 100,000,000) = 1.000001 SOL

Why Linear?

Linear curves provide:

• Predictability: Easy to calculate future prices
• Fairness: Gradual price increases
• Stability: No sudden price cliffs

Market Cap Calculation

Market cap = Token price × Circulating supply

At any point on the curve, you can calculate:

• What buying X tokens will cost
• What selling X tokens will return
• Implied market cap

Liquidity Mechanics

The bonding curve IS the liquidity. No LPs needed. The protocol holds SOL reserves equal to all purchases minus fees. This guarantees you can always sell.

Reserve Formula

Reserve = ∫(Price)dSupply = BasePrice×Supply + (Slope×Supply²)/2

Graduation Trigger

When the bonding curve collects 85 SOL in reserves (minus fees), the token "graduates" to Raydium with real liquidity pools.

Arbitrage Prevention

The bonding curve eliminates arbitrage opportunities because there's only one market maker: the curve itself. Price is deterministic based on supply, preventing front-running and sandwich attacks common on DEXes.

Slippage

Large trades still experience slippage because buying tokens increases price during the trade. The UI shows expected price impact before confirming.