What is a bonding curve? (memecoin launchpads explained)

By the arky team · Updated 4 October 2026

The problem a bonding curve solves

A brand-new token has no market. On a normal decentralised exchange, someone has to deposit both the token and a matching amount of money into a liquidity pool before anyone can trade, and that person sets the starting price. For memecoins, which start with nothing, this cold start is the hardest part.

A bonding curve removes it. The launchpad contract itself is always ready to sell you tokens or buy them back, at a price given by a public formula. The money from buyers stays in the contract as a reserve, which is what sellers are paid from.

How the formula works

The most common choice, used by pump.fun (pump.fun docs) and by arky's launchpad, is the constant-product formula familiar from Uniswap:

x × y = k

• x is the curve's money reserve (USDC on arky), including a virtual starting amount that sets the opening price.
• y is the curve's token reserve, also with a virtual part.
• k stays constant through every trade (before fees).
• The spot price is x / y, in USDC per token.

When you buy, USDC goes in, so x grows. To keep k fixed, y must shrink, and the difference is the tokens you receive. Because y shrinks faster as x grows, every buy pushes the price up, and big buys get a worse average price than small ones. Selling runs the same maths in reverse.

A worked example

The numbers below are illustrative only, chosen to make the arithmetic easy. They are not arky's curve parameters, and fees are left out.

Say a curve starts with a virtual reserve of x = 1,000 USDC and y = 1,000,000,000 tokens. So k = 1,000,000,000,000 and the opening price is 1,000 / 1,000,000,000 = 0.000001 USDC per token.

Three things to notice:

1. Bob paid the same 100 USDC as Alice but got about 17% fewer tokens, because he bought later on the curve.
2. Alice made about 18 USDC by selling after Bob bought. Early buyers profit from later buyers; that is the whole game, and it cuts both ways.
3. After Alice sold, Bob's tokens are worth less than he paid. On a bonding curve the exit price always depends on who else is still buying.

Graduation: leaving the curve

A launchpad does not keep coins on the curve forever. Each curve has a graduation threshold, usually a target amount of money in the reserve. When a buy reaches it, curve trading stops and the reserve, with the remaining tokens, seeds a regular DEX pool.

On arky, graduation moves the coin to a full-range Uniswap v4 pool on Arc. The liquidity is locked permanently, a buy that would overshoot the threshold is filled up to it and the rest refunded, and the coin keeps trading inside arky. Most memecoins never get there, so treat graduation as a milestone, not a promise.

Bonding curve vs liquidity pool

Why the currency of the curve matters

A curve priced in SOL or ETH makes every coin a double bet on the memecoin and the base token. arky's curves are priced in USDC, and Arc pays gas in USDC too (Arc docs), so the price you see is a dollar price. See the memecoin launchpad on Arc and arky vs pump.fun for how that plays out, or go straight to launching your own coin.