What a big first buy does to a pump.fun price

Most markets hide price impact inside an order book you cannot see. A pump.fun coin that has not migrated yet does not have an order book at all. It has a bonding curve: a formula that sets the price from how much SOL is in the curve. That makes one question unusually easy to answer. When a large wallet buys first, what happens to the price for everyone behind it?

The short answer

On a pump.fun style curve, the price is proportional to the square of the SOL held in the curve's virtual reserve. Add 10% more SOL and the price rises about 21%. That squaring is why early buys move the price so violently, and why copying a first buy always costs you something.

These are worked examples, not measurements of any wallet. The method is below, so you can redo it with other numbers.

How the curve sets the price

pump.fun's standard curve is a constant product on virtual reserves. The curve starts as if it held some SOL and some tokens, and it keeps their product constant: virtual SOL × virtual tokens = k. The widely documented launch values are about 30 virtual SOL against about 1.073 billion virtual tokens, out of a total supply of 1 billion.

The price of one token is the ratio of the two reserves. Because the product is fixed, you can rewrite that ratio as price = virtual SOL² ÷ k. That is the whole trick. The price depends on the square of the SOL side.

So a buy of B SOL into a curve holding V virtual SOL moves the price by ((V + B) ÷ V)² − 1. Fees change the decimals slightly. They do not change the shape.

The same buy moves a young curve far more than an older one. A first buy is the most price-moving trade a coin will ever see, pound for pound.

What that means for the second buyer

Say a wallet you copy buys 5 SOL into a fresh curve. Their average price sits somewhere between the start and the end of their own move. Yours starts after their move. On the table above, you are entering roughly a third above where they started, before your own buy adds a bit more.

Then add everyone else. If other people are copying the same wallet, by bot or by hand, some of them land before you. Every one of them pushes the curve further up the square. The queue matters as much as the wallet.

The exit follows the same formula

Selling runs the curve backwards. When a large holder sells, SOL leaves the curve and the price falls with the square of it. A wallet that bought 5 SOL early and sells it all can take a large bite out of the price in one transaction.

That is why copying the sell matters more than copying the buy. If the wallet you follow exits and you do not, you are holding a coin whose price has just been cut by the same arithmetic that lifted it. Being a few seconds late on the exit costs you. Missing the exit entirely is how copytrading turns into bag holding.

What the curve does not tell you

• It says nothing about demand. The formula gives the price for a given amount of SOL. Whether more SOL arrives is the whole trade, and no formula knows.
• It stops at migration. When the curve's token allotment is sold, the coin graduates to a liquidity pool. From then on, impact depends on pool depth. See what happens when a coin migrates.
• Parameters can change. pump.fun has adjusted its product before. The squaring comes from the constant product design. The exact starting values could move.
• Fees are ignored. Every buy and sell pays fees on top. They shave a little off every leg.

How to check it yourself

Open any fresh coin on pump.fun and watch the trades tab. Note the SOL size of an early buy and the market cap before and after it. Plug the numbers into ((V + B) ÷ V)² − 1, with V starting near 30 plus the SOL already bought. It should land close, with fees accounting for the gap. If it does not, the parameters have changed and the table above needs redoing.

What we do with it

Three practical rules fall out of the arithmetic:

1. Speed is worth the most on young curves. The earlier the curve, the steeper the square, and the more every second of delay costs. copypump watches the chain and copies within seconds of the wallet you pick for this reason.
2. Size so the jump is survivable. A fixed amount per trade, or a percentage of theirs with a hard cap. Either way, decide it before the trade where the insider's entry was huge and yours lands far above it.
3. Copy the sell. The exit runs the same formula in reverse, and you want to be on the same side of it as the wallet you copy.

For picking the wallet in the first place, see which pump.fun traders are worth copying.