5: Bonding curve mathematics

Constant Product Formula

Core Principle: x * y = k (constant)

LaunchLab uses a constant product bonding curve similar to Uniswap V2. However, LaunchLab uses virtual reserves and real reserves to control the curve shape and fundraising goals.

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Reserve System

Each pool has 4 reserve values:

Reserve	Symbol	Description
Virtual Base	VA	Virtual token reserves (controls initial price)
Virtual Quote	VB	Virtual SOL reserves (controls initial price)
Real Base	RA	Actual tokens in the pool
Real Quote	RB	Actual SOL raised

Initial Price: P_initial = VB / VA

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1

Buy (Buying tokens with SOL)

Formulas:

Input Reserves (inR) = VB + RB
Output Reserves (outR) = VA - RA

Effective Quote (after fee) = amountIn * (10000 - feeBps) / 10000

Tokens Out = (outR * effectiveQuote) / (inR + effectiveQuote)

Example:

Given:

• Virtual Quote (VB) = 30,000,000,000 lamports (30 SOL)

• Virtual Base (VA) = 793,100,000,000,000 (793,100 tokens, 6 decimals)

• Real Quote (RB) = 0 (no purchases yet)

• Real Base (RA) = 0

• Fee = 1.05% (105 bps)

• Amount In = 1,000,000,000 lamports (1 SOL)

Calculation:

inR = 30,000,000,000 + 0 = 30,000,000,000
outR = 793,100,000,000,000 - 0 = 793,100,000,000,000

effectiveQuote = 1,000,000,000 * (10000 - 105) / 10000 = 989,500,000

tokensOut = (793,100,000,000,000 * 989,500,000) / (30,000,000,000 + 989,500,000)
         = 784,481,793,530,905 / 30,989,500,000
         = 25,312,138,728 (≈ 25,312 tokens)

2

Sell (Selling tokens for SOL)

Formulas:

Input Reserves (inR) = VA - RA
Output Reserves (outR) = VB + RB

Effective Tokens (after fee) = tokensIn * (10000 - feeBps) / 10000

SOL Out = (outR * effectiveTokens) / (inR + effectiveTokens)

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Price Impact

Price impact measures how much your trade affects the price:

Price Before = outR / inR
Price After = (outR - amountOut) / (inR + effectiveIn)
Impact % = ((Price Before - Price After) / Price Before) * 100

Fees are applied to the input amount (SOL or tokens) and the effective amount after fee is used in the bonding curve formulas above.