Pump.fun Bonding Curves Explained: What Graduation Changes

Every Pump.fun coin starts life on a bonding curve, and most people aping into those coins never look at what that actually means. There's no pool somebody seeded and no market maker on the other side. There's a formula. That formula decides two things every trader in the trenches cares about: how much the next token costs you, and what happens to the liquidity when the coin "graduates."

This is the plain-words version of the Pump.fun bonding curve: how it prices a trade, why the last tokens on the curve cost so much more than the first ones, what graduation to PumpSwap really changes, and what the curve can't protect you from. The mechanics come from Pump's own bonding curve page and its public program docs, so you can check me.

What is the Pump.fun bonding curve, in plain words?

Pump describes it as a constant-product AMM, the same family of math Uniswap uses. Two reserves, SOL and the coin, are multiplied together, and that product has to stay constant. Every buy puts SOL in and takes coins out, so the price goes up. Every sell does the reverse, so the price goes down. Per Pump's docs, price impact scales with trade size, and there's no orderbook or off-chain matching at all.

The trick is the word "virtual." A brand-new coin has no real SOL behind it, so the program starts each curve with synthetic reserves. The program README spells it out: on each buy, the virtual and real SOL reserves rise by the same amount while the virtual and real token reserves fall by the same amount. Sells run it backwards. The virtual part sets the price; the real part is what's actually sitting in the curve. That's how a coin is tradable from its first second without anyone putting up liquidity.

What are the starting numbers?

The README shows the program's global settings, which every new coin copies when it's created. In that snapshot:

• Virtual SOL: 30 SOL to start, with zero real SOL.
• Virtual tokens: 1.073 times the coin's total supply.
• Real tokens on the curve: 79.31% of total supply. That's the part you can actually buy from the curve.
• Held back: the other 20.69% never trades on the curve. It's what goes into the pool at graduation, together with the SOL the curve collected.

One caveat up front: these are settings in a global account that an update authority can change, and Pump has added newer trade versions and non-SOL pairings over time. Treat everything below as the math for the standard SOL-paired setup in the docs, not a promise about any specific coin.

Why do the last tokens cost so much more than the first?

Because a constant-product curve gets steep as you drain one side. I ran the numbers from those documented starting values (my arithmetic, before fees and rounding):

• The first quarter of the curve's tokens takes about 6.8 SOL of buying.
• Half the curve takes about 17.6 SOL in total.
• Three quarters takes about 37.3 SOL.
• The whole curve takes about 85 SOL.

So the last quarter of the tokens costs roughly 47.7 SOL, more than everything before it combined. By the end, the price per token is about 14.7 times the starting price.

A worked example

Hypothetical, same math. A 1 SOL buy on a fresh curve gets you about 3.46% of the total supply. The same 1 SOL near the very end of the curve gets you about 0.25%. Same ticket, roughly fourteen times fewer tokens.

That's why "early" on a curve is structural, not skill. Whoever buys in the first blocks sits on a cost basis late buyers can't get, no matter how good their read is. When those early wallets sell, they sell into the same curve, pushing the price back down it. I wrote more about how that plays out in why most Solana meme coin traders lose money.

What does graduation actually change?

Graduation is mechanical. Per the README, a buy that leaves zero real tokens on the curve flips a complete flag to true. After that, a migrate instruction moves the liquidity into a PumpSwap pool. Two details matter:

• Anyone can trigger it. Migration is permissionless and idempotent, so there's no team member who has to press a button, and running it twice does nothing. The old withdraw path, where an authority moved liquidity to Raydium from an off-chain server, is disabled.
• The LP tokens are burned. The README says the LP tokens from the new pool are burnt, and Pump's page says it doesn't seed or remove that liquidity afterwards. If you want the difference between burned and locked LP, my LP locked vs burned guide covers it.

Here's a part people miss. With the documented settings, the roughly 85 SOL raised plus the 20.69% held-back supply opens the pool at about the same price the curve ended on (my arithmetic, before migration costs). Graduation isn't built to be a price jump. What changes is the venue: you're now trading against an AMM pool instead of the curve. Pump lists the curve's total trading fee at 1.25% and publishes a separate fee schedule for PumpSwap. The public docs repo also notes that, with newer buy versions, the one buy that crosses the finish line can take the remaining tokens at the pool's price, and nothing else trades on the curve until migration runs.

What the curve doesn't protect you from

A bonding curve fixes the cold-start liquidity problem. It doesn't fix people.

• No LP to pull isn't the same as safe. Before graduation, the curve holds the reserves, so the classic liquidity rug isn't the play. The risk moves to who holds the supply and how fast they sell. My post on suspicious activity in new token launches goes through what to check.
• Burned LP doesn't stop the price falling. It means the starting liquidity can't be withdrawn. Holders can still sell into the pool all day. Depth and demand are different things, as I covered in market cap vs liquidity on Solana.
• Graduation isn't a quality badge. It means about 85 SOL of net buying went into the curve. Coordinated or bundled buys can get it there too.
• The math is before costs. Fees and your slippage setting sit on top. On a steep curve, a big order eats a lot of impact, which I broke down in slippage vs price impact.

How to use this in the trenches

• Know where it sits on the curve. How much of the curve is already filled tells you what slope you're buying on. Near the end, the same SOL buys far less.
• Size for the slope. Late on the curve, a sell from one larger early holder moves the price further against you than the chart makes it feel.
• Read your real fill. After the buy, check the balance changes on the explorer instead of trusting the toast. How to read a Solana transaction walks through it.
• Check the holders, not just the curve. The curve tells you price. Wallets tell you who's about to sell. Start with how to analyze a Solana wallet before buying.

The takeaway

The Pump.fun bonding curve is just constant-product math with virtual reserves, and that math is steep: on the documented settings, the last quarter of the curve costs more SOL than the first three quarters combined. Graduation moves the liquidity into a pool and burns the LP, but it doesn't reset anyone's cost basis or change who's holding. Know which part of the curve you're buying on before you buy. When you look at a fresh coin, do you check how far along the curve it is, or just the chart?

Still building. Still here. 🫡