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The pump.fun bonding curve: the math behind every launch

How pump.fun works: every coin trades on its own bonding curve until about 85 SOL of buys. The formula, what 'progress' means, and a 1 SOL buy worked through.

Updated OCTOBER 6, 2026· Fullport Capital

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How pump.fun works, in short#

Pump.fun works by giving every new coin its own bonding curve: a formula that sells the coin's tokens for SOL and raises the price with every buy. Anyone can launch a coin for free and trade it immediately. When about 85 SOL of real buys has gone in, the coin graduates to a PumpSwap pool.

  1. 1

    A creator launches the coin

    pump.fun's program mints a fixed supply of 1 billion tokens and opens a curve for it. Nobody has to seed a pool with their own money.

  2. 2

    Traders buy and sell against the curve

    There is no order book and no liquidity provider. You trade against a program account holding the unsold supply and the SOL buyers have paid in.

  3. 3

    The price follows the formula

    Every buy adds SOL and removes tokens, so the price rises; every sell does the reverse. The progress bar fills as the curve's tokens are sold.

  4. 4

    The curve completes and the coin graduates

    When the last curve token is sold, the coin's SOL and reserved tokens move to a pool on PumpSwap, and the curve closes for good. See pump.fun graduation.

The curve is the reason pump.fun works the way it does: free launches, instant trading, and a price that starts very low. Everything below is from pump.fun's published program documentation and fee page as of October 2026, linked where each number appears.

The formula: x·y=k on virtual reserves#

pump.fun's program docs describe the curve as a constant-product market in the style of Uniswap V2, with virtual reserves. Constant product means the SOL reserve multiplied by the token reserve stays equal to a fixed number, k. The price at any moment is simply SOL reserve ÷ token reserve.

Why does the curve use virtual reserves?

A real pool with zero SOL in it would have no price at all. So every pump.fun curve starts with reserves the program treats as if they were there:

ParameterValueWhat it means
Initial virtual SOL reserve30 SOLNot real SOL; it sets the starting price and depth
Initial virtual token reserve1,073,000,000Also partly virtual
Real tokens for sale on the curve793,100,000When these are gone, the curve is complete
Total supply1,000,000,000Fixed; the rest is reserved for the pool at graduation
k (virtual SOL × virtual tokens)≈ 32.19 billionConstant on every trade

Swipe or scroll to compare all columns.

Values from the Global account in pump.fun's program docs, checked October 2026. Token counts are shown without the 6 decimals the program stores.

Where does a pump.fun coin start and finish?

The starting price is 30 ÷ 1,073,000,000 SOL per token, which puts the coin's market cap at about 28 SOL before anyone buys (about $4,200 at an illustrative $150 per SOL). After 85 SOL of real buys, the virtual SOL reserve is 115 and the token reserve has fallen to about 279.9 million.

At that point the real token reserve hits zero. That is graduation, at a market cap of about 411 SOL.

One rule of thumb

Because both reserves move, market cap on a pump.fun curve grows with the square of the virtual SOL. It is (30 + real SOL in)² ÷ 32.19, in SOL. Double the virtual SOL and the market cap quadruples.

What the progress bar actually measures#

The bonding-curve progress bar tracks how much of the 793.1 million sellable tokens have been bought. It is not a percentage of SOL raised, and it does not move in step with price. The first few SOL buy a lot of tokens cheaply, so the bar fills fast early and slowly late.

Real SOL in the curveProgressMarket cap
00%28 SOL ($4.2k)
519%38 SOL ($5.7k)
1034%50 SOL ($7.5k)
2054%78 SOL ($11.7k)
4077%152 SOL ($22.8k)
6090%252 SOL ($37.7k)
85100%411 SOL ($61.6k)

Swipe or scroll to compare all columns.

Computed from the published starting reserves with x·y=k, dollar figures at an illustrative $150 per SOL. Real SOL excludes fees, which are paid on top and do not stay in the curve.

Two things stand out. A coin that is "half way" on the bar has taken in only about 18 SOL, a fifth of what it needs.

And the move from launch to graduation is about 14.7× in price, no matter how fast or slowly it happens. A trader who bought the very first token and held to graduation made at most that multiple, before fees.

What a 1 SOL buy does to the curve#

Every buy moves the price against the buyer while it fills. The same 1 SOL does very different things depending on how much is already in the curve, because early on the virtual reserves are thin. The table assumes the 1.25% curve fee is taken out of the 1 SOL before the swap.

Real SOL already inAverage fill vs pre-trade pricePrice after your buy
0 (first buy)+4.6%+6.7%
10+3.8%+5.0%
40+2.7%+2.8%
80+2.2%+1.8%

Swipe or scroll to compare all columns.

Average fill includes the 1.25% fee. Constant-product math on the published starting reserves. The first buy receives about 34.2M tokens; at 80 SOL in, about 2.6M.

What does a round trip on the curve cost?

Buy 1 SOL at 10 SOL in and sell the same tokens straight back, with nobody trading in between, and you get back about 0.975 SOL. The price impact reverses; the two fees do not. A round trip on the curve costs about 2.5% plus two network fees even when the chart has not moved.

How much does pump.fun charge, and how does it make money?

pump.fun's fee page (last updated 20 May 2026) puts the curve fee at 1.25% on every buy and sell: 0.95% to the protocol and 0.30% to the coin's creator, with nothing to liquidity providers because there are none. That creator share is what pump.fun calls creator rewards. pump.fun also charges 0.015 SOL at graduation and keeps a protocol share of PumpSwap fees afterwards.

Trading terminals usually add their own fee on top, and Solana charges a base fee plus whatever priority fee you set. The paper trading vs funded account article works through a $500 buy with all of those included.

What the curve does and does not protect you from#

The curve design removes some classic scams and leaves others untouched. Knowing which is which matters more than the formula.

  • No liquidity pull. The SOL in a curve is held by the program, not the creator. Nobody can withdraw it, so the old rug pull where a developer removes the pool cannot happen on the curve.
  • Fixed supply. The supply is set by the program at 1 billion. The creator cannot mint more mid-curve.
  • You can always sell back to the curve. As long as it has not completed, there is a bid. Selling a large bag into a thin curve is expensive, but it is never blocked by the curve itself.
  • Supply concentration is not prevented. A creator can buy in the creation transaction, and wallets can buy in the same block through bundles. If a handful of wallets hold a third of the supply, they can sell it into you. See bundled supply.
  • Momentum is not information. A fast-filling bar says SOL is arriving, not who is sending it or why.

In other words, a pump.fun rug is a supply dump, not a liquidity pull. How not to get rugged covers the patterns, and whether pump.fun is safe to trade at all.

Trading the curve on a simulated funded account#

Fullport prices pump.fun curve trades with the same math pump.fun uses. The engine reads the coin's bonding-curve account fresh at execution, after a modeled 250 ms delay, and quotes your order through pump.fun's own SDK functions.

The fill charges the 1.25% curve fee, a modeled network fee, Fullport's 1% platform fee and your own price impact, as listed on the fill policy. Orders that would move the price more than 15% are rejected under the impact cap.

Your cost is capped at the one-time fee of $120, $195 or $300 for a $25,000, $50,000 or $125,000 account: trading losses come out of the simulated balance, never your wallet. Pass the +6% target while staying above the single 4% floor, and funded payouts send you 80% of profit in SOL. Trade from the browser terminal or on pump.fun's own page with Fullport Tap; the workflow is in how to get funded to trade pump.fun.

Quick answers

How does the pump.fun bonding curve work?
Each coin trades against its own constant-product curve with virtual reserves of 30 SOL and 1.073 billion tokens. Buying adds SOL and removes tokens, so the price rises. When all 793.1 million sellable tokens are bought, about 85 SOL later, the curve completes and the coin moves to PumpSwap.
What is the starting market cap of a pump.fun coin?
About 28 SOL, from the published starting reserves: 30 SOL divided by 1.073 billion tokens, times the 1 billion supply. At an illustrative $150 per SOL that is roughly $4,200. The dollar figure changes with the SOL price; the SOL figure does not.
What does bonding curve progress mean on pump.fun?
It is the share of the 793.1 million curve tokens that have been sold. It fills fast early because the first SOL buys many cheap tokens: 50% progress is reached after only about 18 SOL of the roughly 85 SOL needed to graduate.
How does pump.fun make money?
From trading fees. On the bonding curve pump.fun keeps 0.95% of every buy and sell, with another 0.30% going to the coin's creator. It also charges 0.015 SOL when a coin graduates and takes a protocol share of PumpSwap pool fees afterwards, per its fee page.
Can a developer rug a coin on the pump.fun bonding curve?
Not by pulling liquidity, because the curve's SOL is held by the program. But a developer or a bundle of linked wallets can buy a large share of the supply cheaply at launch and sell it into later buyers, which has the same effect on your position.