The pump.fun bonding curve explained: why the first buyers pay less, and what “graduation” means
Key takeaways
- The curve is arithmetic, not a market. Two virtual reserves, 30 SOL and 1.073 billion tokens, are multiplied together; every trade has to keep that product constant.
- About 85.0 SOL graduates a coin. That is the net buying needed to sell all 793.1 million tokens on offer; the market cap at that moment is about 411 SOL.
- Late money buys little. The first 42.5 SOL buys 79% of the curve’s tokens; the next 42.5 SOL buys only 21%.
- Graduation is a mechanical event, not a quality signal. It means enough SOL went in, nothing more.
- You can always sell on the curve, at whatever price the sellers before you left. Buy 1 SOL at 75% sold, and if holders sell back to half, your tokens fetch 0.48 SOL.
What is a bonding curve, in one paragraph?
A bonding curve is a price formula that stands in for a market when a coin is too new to have one. pump.fun’s documentation says it plainly: “There is no orderbook, no market-makers, and no off-chain matching. The price you pay is a pure function of how many tokens are in circulation.” The specific formula is a constant-product one — the same family as a Uniswap pool. Two reserves, one of SOL and one of the coin, are multiplied together, and every trade must leave that product unchanged. Put SOL in, and the formula hands out fewer and fewer tokens per SOL as the token reserve shrinks.
The word that matters in the highlighted sentence is virtual. A brand-new coin has no real SOL in its pool. If the formula started from zero SOL, the first buy would divide by zero. So the program starts the curve with pretend reserves — SOL that nobody deposited and tokens that will never be sold — purely to give the formula a starting price. Those starting numbers decide everything else on this page, and pump.fun publishes them.
What are the actual numbers behind the pump.fun curve?
The program’s public documentation on GitHub lists the starting values of its global settings. Three of them define the curve: 1.073 billion virtual tokens, 30 virtual SOL, and 793.1 million real tokens for sale. The total supply of every coin is 1 billion.
From those three numbers the rest follows, and this is the part we could not find written anywhere in pump.fun’s pages, so we did the arithmetic ourselves:
- The constant. 30 SOL × 1.073 billion tokens. Every trade on the curve keeps this product the same.
- The first price. 30 SOL divided by 1.073 billion tokens: about 0.028 SOL per million tokens. Multiply by the 1 billion supply, the way pump.fun’s fee page says market cap is counted, and a new coin starts at a market cap of about 28 SOL — with zero SOL actually in it.
- The end of the curve. When all 793.1 million real tokens are sold, the virtual token reserve is down to 279.9 million. Holding the product constant, the SOL side has to be about 115.0 SOL, which means buyers have put in about 85.0 SOL of real money (after fees). That is the graduation point.
- The last price. 115.0 SOL over 279.9 million tokens: 14.7 times the first price. The average price paid across the whole curve is 3.8 times the first.
The program documentation describes the end condition in its own words: the curve is marked complete “when real_token_reserves == 0, so there are no more real tokens left in the bonding curve”. pump.fun’s help page describes the same moment as the market cap reaching a “graduation threshold” without giving the figure; our 411 SOL is that threshold as implied by the published parameters.
One honest caveat. The same GitHub file lists a 1% fee setting, while pump.fun’s fee page, last updated 20 May 2026, says 1.25%. The fee page is the newer document, so we used 1.25% — but the gap is a reminder that these settings can be changed, and the coin page you are looking at is the final word on what you pay.
Why do the first buyers pay less?
Because on a curve, your price is set by how much SOL went in before you. Here is what a single SOL buys at different points on the same coin’s curve, with the 1.25% fee taken off the way in.
| Where the coin is on the curve | SOL already put in by buyers | Price vs the first buy | Market cap (price × 1B) | Tokens 1 SOL buys |
|---|---|---|---|---|
| The very first buy | 0.0 SOL | 1.00x | 28 SOL | 34.2M |
| A quarter of the tokens sold | 6.8 SOL | 1.50x | 42 SOL | 22.9M |
| Half sold | 17.6 SOL | 2.52x | 70 SOL | 13.8M |
| Three quarters sold | 37.3 SOL | 5.04x | 141 SOL | 6.9M |
| 90% sold | 59.6 SOL | 8.92x | 249 SOL | 3.9M |
| Last buy before graduation | 85.0 SOL | 14.7x | 411 SOL | — |
Read the last column down. The same 1 SOL buys 34.2 million tokens on the first trade and 3.9 million once 90% of the curve has sold — roughly a ninth as many. Nothing about the coin changed between those two rows. Only the amount of SOL ahead of you did.
The chart shows the shape that the table hides. The curve does not jump at the start and level off; it gets steeper. The first 42.5 SOL — half of all the money the curve will ever take — buys 79% of the tokens. The second 42.5 SOL buys the remaining 21%. That is the whole “early buyers pay less” effect, and it is not a perk anybody grants: the people who bought late are the ones paying the early buyers’ gain.
What does “graduation” mean, and what changes after it?
Graduation is the moment the last curve token is sold. pump.fun’s page says the curve is then closed and “the entire liquidity pool is migrated atomically to PumpSwap”, its own exchange, and that it is “automatic and irreversible. There’s no human step.” The SOL in the curve and the tokens that were never on sale — the other 206.9 million of the 1 billion supply, as we read the parameters — become the coin’s pool. The docs say pump.fun does not add or remove that liquidity afterwards and the pool is owned by the protocol; the program documentation adds that the pool’s LP tokens are burnt.
Two things on that fee page are worth connecting to the curve maths, because nobody else connects them:
- Graduation costs 0.015 SOL (box 1), taken when the coin moves to PumpSwap.
- The fee does not drop the moment a coin graduates. On the curve it is 1.25% (box 2). On PumpSwap, the fee for a coin’s main pool depends on market cap, and the first tier, 0 to 420 SOL, is also 1.25%. Our graduation market cap is about 411 SOL — inside that first tier. So a freshly graduated coin keeps charging the same 1.25% until its market cap climbs past 420 SOL.
What graduation does not mean is just as important. It is not a review, a listing decision or a sign of quality. It is a counter reaching a number. A coin that graduates has had about 85.0 SOL of net buying; it can be sold down on PumpSwap the next minute like any other pool.
What does the curve mean for the money you put in?
Two things, one reassuring and one not. The reassuring one first: while a coin is on the curve, there is always someone to sell to. The SOL that buyers put in sits in the curve, and the formula will always pay some of it out for your tokens. A coin on the curve cannot simply have no buyers.
The other one is price. The formula pays out whatever SOL is left at the point you sell. If you are the only trader, buying and selling straight back costs you only the fees. If others sell before you, it costs a great deal more. We bought 1 SOL of a hypothetical coin at 75% sold, on paper, and asked what it sells for after other holders have sold first:
| After you buy 1 SOL at 75% sold, other holders sell until… | What your tokens sell for | Change |
|---|---|---|
| Nobody else trades; you sell straight back | 0.975 SOL | −2.5% (fees only) |
| Back to half sold | 0.475 SOL | −52% |
| Back to a quarter sold | 0.285 SOL | −72% |
| Everyone else sells out | 0.190 SOL | −81% |
That last row is the curve’s honest worst case: even if every other holder sells before you, you still get something back — 0.19 SOL of your 1 SOL. The middle rows are the ordinary case. A coin bought at three-quarters sold that slips back to half sold has cost you more than half of your stake, with no “crash” and no foul play, just ordinary selling. This is the arithmetic behind the line on our pump.fun profile: size every buy as money you expect to lose in full.
Anyone still learning to trade. A bonding curve rewards being early and punishes being late, which teaches you to chase. Learn on a market where price reflects supply and demand you can reason about — the Primer Path is built for that, and the exchange comparison is where to open a first account.
Anyone who has not used a self-custody wallet. pump.fun runs on Solana from your own wallet; a lost seed phrase or a bad signature is final. Our self-custody checklist comes first.
Anyone who would add more after a loss. The table above is what “averaging down” looks like on a curve: each new buy is priced by everyone ahead of you.
IF YOU STILL WANT TO TRY IT
Affiliate disclosure first: the button below is a referral link. pump.fun may pay us if you sign up through it, at no cost to you. It changes nothing on this page — see our disclosure policy.
Decide the sum before you open the site, and treat it as gone. You hold the keys there, so a lost seed phrase is lost money and there is nobody to ask for it back. Look at how far along the curve a coin already is before you buy: the later it is, the less your SOL buys and the more you depend on people buying after you.
Referral link — we may be paid if you open an account through it. Readers in the UK see no venue links on this site. Memecoins can and usually do lose the whole stake. Education only.
Common mistakes
- Reading the market cap as money in the coin. A brand-new coin shows a market cap of about 28 SOL with no SOL in it at all; the virtual reserves create that number.
- Treating graduation as an endorsement. It means about 85.0 SOL went in. Nobody looked at the coin.
- Expecting lower fees right after graduation. The first PumpSwap tier, up to 420 SOL market cap, is the same 1.25% as the curve.
- Thinking a sell is safe because the curve always buys. It always buys — at the price left by the sellers ahead of you.
- Buying late because the price is “still going up”. Near the end, each SOL buys a ninth of what it bought at the start. You need more buyers after you, not fewer.
- Using the numbers on this page for a USDC-paired coin. We modelled SOL-paired coins only.
Frequently asked questions
What is a bonding curve on pump.fun?
It is the pricing rule a new coin trades on before it has a market. pump.fun’s docs describe it as a constant-product AMM with two virtual reserves, SOL and the coin’s supply, multiplied together to form an invariant. Every buy moves the price up and every sell moves it down, with no order book and no market-makers.
How much SOL does it take for a pump.fun coin to graduate?
On the program’s published starting parameters, about 85.0 SOL of buying (net of the 1.25% fee) sells all 793.1 million tokens on the curve. At that point the market cap is about 411 SOL and the coin moves to PumpSwap automatically. These are our calculations from the published parameters, which can change.
What happens when a coin graduates?
The curve closes and its SOL and remaining tokens become the coin’s pool on PumpSwap, which the docs say is owned by the protocol; the program documentation says the pool’s LP tokens are burnt. A 0.015 SOL graduation fee applies. Graduation is automatic and cannot be reversed, but it does not mean anyone will keep buying.
Why do early buyers pay less?
Because the curve’s price is a function of how much SOL has gone in. On the published parameters the last price on the curve is 14.7 times the first, and the first half of the money buys 79% of the tokens. Every later buyer is paying a higher price set by everyone before them.
Can I always sell on the bonding curve?
While the coin is on the curve, yes: the SOL buyers put in sits in the curve, so a sell always has a counterparty. What you cannot control is the price. If other holders sell first, your tokens buy back far less SOL, as the scenario table on this page shows.
Keep going: the pump.fun profile, FOMO, the same market with a leaderboard, what a DEX is, DEX vs CEX and why most new traders lose money in year one.