Formula & Calculator
Linear Bonding Curve Price
Calculates a token's price on a linear bonding curve, where price increases predictably as more tokens are minted from the curve.
Interpretation
Price = m × Supply + b. A linear bonding curve relating token price to supply. Used in token sales and automated market making.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Price | Current token price | currency |
| m | Curve slope | |
| Supply | Current token supply issued from the curve | |
| b | Base price (y-intercept) | currency |
What it means
A bonding curve defines the relationship between token supply and price. A linear curve is the simplest: price increases linearly with supply. This is used in token sales (e.g., for DAOs) and in some AMMs. Understanding bonding curves helps in designing token economics and in predicting price behaviour.
Worked example
Linear Bonding Curve Price – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Slope (m) | 0.0001 |
| Current Supply | 10,000 |
| Base Price (b) | 0.01 |
| Parameter | Value |
|---|---|
| m | 0.00005 |
| Supply | 50,000 |
| b | 0.05 |
Common mistakes
- Linear bonding curve: Price = m × Supply + b – price increases with supply.
- m: The slope of the curve.
- b: The intercept (starting price).
- Buy/sell: The price determines the cost to buy or sell tokens.
Applications
Linear bonding curve price calculates the price of a token based on its supply, using a linear function. This is used in some token sales and decentralised marketplaces. By understanding the price formula, users can predict price changes as supply changes. This is fundamental to bonding curve economics.
- Pricing tokens in bonding curve sales
- Designing token economics with linear curves
- Predicting price impacts of buying/selling
- Educational understanding of bonding curves
Frequently Asked Questions
Price = m × Supply + b. For example, if m = 0.0001, Supply = 10,000, and b = 0.01, the price is 0.0001×10000 + 0.01 = 1.01. This means the price rises as more tokens are minted.
The slope determines how quickly the price increases with supply. A higher m means price rises faster with each new minted token. It is a key parameter set by the curve designer.
The base price is the price when supply is zero. It sets the starting price. In practice, b is often set to a small positive value to prevent the price from being zero.
Not necessarily. Some bonding curves have separate buy and sell curves (a spread) where the sell price is slightly lower than the buy price. This creates a profit margin for the curve.
Bonding curves provide a transparent, deterministic pricing mechanism for token sales. They eliminate the need for traditional order books and ensure liquidity.
It directly ties token price to supply, creating a deflationary or inflationary pressure. As more tokens are bought, price increases, which can create a feedback loop.
Usually not, because changing them could affect the integrity of the curve. Some designs allow governance to change parameters, but this is rare.
A linear curve increases price linearly with supply. Polynomial or exponential curves have different shapes, leading to faster or slower price increases. Each suits different use cases.