pump.fun explained: the bonding curve, graduation, and what one trade really costs

Posted by the operator of RebateMax

I earn a referral commission from BingX and LBank when you register through my links, and both exchanges list meme coins. I have no relationship with pump.fun or with any trading terminal, and none of them has seen this post. Every pump.fun figure below comes from two of its own documents: its public program documentation, read 3 October 2026, which publishes the numbers every new coin starts with, and its fee page, last updated 8 October 2026. The arithmetic is mine, and I show it so you can check it.

This is the deep version of one section of Memecoin trading, honestly. That post covers the odds, the terminals and who gets paid. This one covers the machine.

The short version

• Every new coin starts on the same curve. One billion tokens, of which 793.1 million are for sale on the curve. The price is set by a formula, not by matching you with another person.
• Early buyers get far more tokens per SOL. The first 40 SOL paid into a curve buys about 613 million tokens. The last 45 SOL buys about 180 million.
• Graduation happens at about 85 SOL. When the last curve token is sold, the coin moves to PumpSwap, pump.fun's own exchange. By then the price is about 14.7 times where it started.
• Your own buy moves the price. On a brand-new coin, a 1 SOL buy gets you 3.2% fewer tokens than the price on the screen suggested.
• The fee is fixed and large. 1.25% per trade on the curve, and a terminal adds about 1%. A $500 buy and sell costs about $22 in fees before the coin has moved.

What a bonding curve is

A normal exchange matches you with another person who wants the other side of your trade. A pump.fun coin starts with nobody on the other side. You trade against a formula instead.

pump.fun's documentation says the formula "is based on Uniswap V2 and uses synthetic x and y reserves." In plain terms: the curve holds two piles, one of SOL and one of tokens, and the price is simply the SOL pile divided by the token pile. When you buy, your SOL goes onto the SOL pile and tokens come off the token pile, so the price rises. When you sell, the reverse happens. The rule that fixes how many tokens you get is that the two piles multiplied together must stay the same.

The word "synthetic" matters. A new coin has no SOL in it at all, so the curve pretends it starts with some. These pretend amounts are called virtual reserves, and they decide the whole shape of the curve.

The numbers every new coin starts with

These are the starting values in pump.fun's program documentation for coins priced in SOL.

From pump.fun's public program documentation, read 3 October 2026. Coins paired with USDC rather than SOL are not covered by these figures.

The 206,900,000 tokens that are not for sale on the curve are held back: at migration they become the token side of the PumpSwap pool, alongside the SOL buyers paid in. That is why the market-cap figures below are worked on the full billion.

From those five numbers, everything else follows. The two piles multiplied together are 30 × 1,073,000,000 = 32.19 billion, and that product never changes on the curve.

The starting price is 30 SOL divided by 1,073,000,000 tokens, which is about 0.000000028 SOL per token. On the full billion tokens, that values a brand-new coin at about 28 SOL.

The end of the curve comes when all 793.1 million sale tokens are gone. The token pile is then 1,073,000,000 minus 793,100,000, which is 279,900,000. To keep the product at 32.19 billion, the SOL pile must be about 115.0 SOL. Take away the 30 pretend SOL and buyers have paid in about 85.0 SOL. That is where the "about 85 SOL" figure for graduation comes from.

The price at the end is 115.0 SOL divided by 279.9 million tokens, about 0.00000041 SOL per token, or 14.7 times the starting price. On a billion tokens, that values the coin at about 411 SOL.

Why the first buyers get so much more

Because the price rises with every purchase, the curve hands out most of its tokens early. Halfway through the SOL is nowhere near halfway through the tokens.

My arithmetic on the published starting values. Fees are left out.

The first 40 SOL buys about 613 million tokens. The remaining 45 SOL buys about 180 million. Whoever buys in the first seconds pays a fraction of what a buyer near graduation pays for the same token, which is what makes being first worth automating. If you are buying by hand, you are almost never the early buyer in that table.

How much your own buy moves the price

On a curve like this, there is a short way to work out how much worse your price is than the one on the screen: divide the SOL you are spending by the SOL pile plus your SOL. That share is how many fewer tokens you receive than the quoted price implied.

My arithmetic: your SOL ÷ (SOL pile + your SOL). Fees are not included and are charged as well.

Two things follow from that. A larger buy into a young coin costs you more per token, sharply so. And the price rise you see straight after your own buy is one you created. If nobody else trades and you sell straight back, the curve returns your SOL less the fees, and nothing more. The rise is only worth something if other people buy after you.

What graduation actually is

The documentation is precise about this. A coin's curve is marked complete at the end of the purchase that sells its last sale token. After that, anyone can trigger the move, which pump.fun calls migration, and the liquidity goes into a pool on PumpSwap. pump.fun's fee page charges 0.015 SOL for the graduation. The documentation also says the pool's liquidity tokens are then burnt, which is meant to stop anyone withdrawing that starting liquidity later.

Before 20 March 2025, graduating coins went to Raydium instead. pump.fun built PumpSwap and moved them in-house, as The Block reported at the time.

Graduation is rare. In a study of pump.fun's first two years by a group of academic security researchers, they tracked 15,245,966 coins and found that 1.02% of the coins in their sample ever left the curve; they have price data for 154,513 graduated coins, which is about 1% of the total. Their paper is peer reviewed and published at ACM CCS 2026, one of the main academic security conferences; the version I read is the authors' arXiv copy. For the other 98.98%, the curve is the whole life of the coin.

What pump.fun charges

The fee page, last updated 8 October 2026, sets one rate on the curve and a sliding rate after graduation.

Selected rows from pump.fun's fee page for coins priced in SOL. The full table has 25 steps. The fee is charged on the buy and again on the sell. The page also notes that pump.fun's own web app, advanced page and mobile app add nothing to the rates above on Solana trades, and that other interfaces may charge their own fees on top - which is the terminal fee in the next section.

Put that next to the curve arithmetic. A coin graduates at a market cap of about 411 SOL, so it arrives on PumpSwap in the most expensive band and pays the same 1.25% it paid on the curve. The first cut, to 1.20%, comes at 420 SOL, barely above where a coin graduates. The fee does not reach 1.00% until about 4,420 SOL, roughly ten times the graduation value, and 0.30% only above 98,240 SOL. A brand-new graduate is not a cheaper trade.

What one $500 trade costs

Most people do not trade on pump.fun's own page. They use a terminal, which adds its own fee. Axiom, the largest, lists 0.95% at its entry tier; GMGN, BullX and Photon each list 1%. Here is a $500 buy followed by a $500 sell through a terminal at 0.95%, set against an exchange.

Fees only, each side charged once, the same method as the flagship post. BingX uses its standard 0.1% spot rate, halved by the referral discount. Price impact, Solana priority fees, tips to land a trade quickly, exchange spreads and withdrawal fees are left out of every row.

So on the curve the coin has to rise by about 4.5% before you break even on fees alone. Then come the two costs the table leaves out.

Price impact and slippage. Take a 1 SOL buy into a coin with 40 SOL already in its curve. pump.fun takes 0.0125 SOL, a terminal at 0.95% takes 0.0095 SOL, and you receive 1.4% fewer tokens than the screen price implied (the table above). If other buyers get in just ahead of you, it is worse. That is what the slippage setting in a terminal is for. pump.fun's documentation shows that a buy names an exact number of tokens and the most SOL you will pay for them, and a sell names the least SOL you will accept. The gap between the screen price and that limit is your slippage setting. Set it wide and you accept up to that much worse a price. Set it narrow and the trade can fail while the curve moves.

Priority fees. On Solana you can pay extra to have your trade processed first, and terminals let you set this. Neither pump.fun nor the terminals publish a standard amount, so I will not print one. The arithmetic is simple: every 0.001 SOL of priority fee is another 0.1% of a 1 SOL trade, and you pay it again on the sell.

The exchange row is not the same trade, and I do not want the table to suggest it is. An exchange lists a coin weeks or months later, if ever, and only after it has survived. You pay less because you are buying something different. The flagship post sets out that trade-off in full, and the fee calculator runs the exchange side on your own numbers.

What to take from this

The curve is not a scam in itself. It is a published formula that anyone can check, and it does what it says. What it does is pay the first buyers in tokens and charge everyone a fixed fee on the way in and on the way out. If you buy by hand, you are usually buying from the part of the curve where the early tokens have already gone, you pay the fee twice whatever happens, and you are betting that more people buy after you than before you.

If you want to watch how memecoins behave once they reach an exchange, our Memecoin Desk measures every coin it covers from the day it is listed, losses included. How we decide which tokens to cover explains what has to be true before we measure one at all.

Questions people ask

How does the pump.fun bonding curve work? It holds a pile of SOL and a pile of tokens and keeps the two multiplied together constant. Each buy adds SOL and removes tokens, so the price rises; each sell does the reverse. A new coin starts with 30 pretend SOL and 1,073,000,000 pretend tokens, which sets its starting price.

How much SOL does it take for a pump.fun coin to graduate? About 85 SOL paid into the curve, for coins priced in SOL. That is the point where all 793.1 million sale tokens have been bought.

What happens when a pump.fun coin graduates? The curve is marked complete, its liquidity moves to a PumpSwap pool, the pool's liquidity tokens are burnt, and 0.015 SOL is charged for the move. Trading carries on in the pool.

What are pump.fun's fees? 1.25% per trade on the bonding curve. On PumpSwap, from 1.25% for coins under 420 SOL of market cap down to 0.30% for the largest, as of the fee page dated 8 October 2026. A terminal adds about 1%.

Why do bots buy pump.fun coins first? Because the curve gives the earliest buyers by far the most tokens per SOL. The first 40 SOL into a curve buys about 77% of the sale tokens.

Sources

• pump.fun, public program documentation (read 3 October 2026): github.com/pump-fun/pump-public-docs. Source for the starting reserves, the supply, the formula, completion, migration and the burnt liquidity tokens.
• pump.fun, fee documentation (last updated 8 October 2026, read 15 October 2026): pump.fun/docs/fees. Source for every pump.fun and PumpSwap fee and the graduation fee.
• The Block, on the move from Raydium to PumpSwap (20 March 2025): theblock.co/post/347360.
• Szwajcok, Tsuchiya, Liu, Soska, Payer and Christin, "Meme Coin Factories: Uncovering Large-Scale Manipulations on pump.fun" (ACM CCS 2026): arxiv.org/abs/2609.10246. Source for the coin count and the graduation rate.
• Axiom, fee tiers (read 21 September 2026): docs.axiom.trade/getting-started/fees/axiom-fees. GMGN, BullX and Photon fee pages as listed in the flagship post.
• BingX spot rates as published and as used in the annual fee math post.

Disclosure: RebateMax earns affiliate commission on trading fees generated by accounts registered through its BingX link and returns 50 of those 60 commission points as a lifetime discount. The full arithmetic is here. RebateMax also earns a referral commission from LBank. It has no commercial relationship with pump.fun, Axiom, GMGN, Photon or BullX. Memecoins are extremely high risk and most go to zero. This post is general information, not financial or tax advice, and nothing here is a recommendation to trade. Think a figure is wrong? See the corrections policy.