Price, tick index and sqrt price correlation calculation
What's difference between price, tick index and sqrt price?
Price
Token exchange ratio (e.g., token1/token0
)
Continuous value, updates in real-time
Directly determines trading rates
Tick Index
Discretized price interval index
Spacing determined by fee tiers
Manages liquidity distribution ranges
Sqrt Price
Square root of price
Stored as fixed-point numbers (e.g., sqrtPriceX64
)
Simplifies on-chain calculations, improves efficiency
Notes:
Price: Represents the real-time ratio between two tokens (e.g., ETH/USDC).
Tick Index:
Derived from
P = 1.0001^i
, wherei
is the Tick Index.Liquidity can only be provided at discrete Ticks (e.g., multiples of 10).
Sqrt Price:
Used for computational efficiency (avoids floating-point operations).
In Uniswap V3, stored as
sqrtPriceX64
(Q64 fixed-point format).
1. Tick index to price
when you want to open position, you dont know how to set your tick_lower and tick_upper.
use /src/math/tick.ts TickMath.
tickIndexToPrice()
import { TickMath } from '@cetusprotocol/cetus-sui-clmm-sdk'
// decimalsA and decimalsB means the decimal of coinA and coinB
const price = TickMath.tickIndexToPrice(tickIndex, decimalsA, decimalsB)
2.Price to tick index
use /src/math/tick.ts TickMath.priceToTickIndex()
import { TickMath } from '@cetusprotocol/cetus-sui-clmm-sdk'
// decimalsA and decimalsB means the decimal of coinA and coinB
const tickIndex = TickMath.priceToTickIndex(price, decimalsA, decimalsB)
3. Tick index to sqrt price x64
use /src/math/tick.ts TickMath.tickIndexToSqrtPriceX64()
import { TickMath } from '@cetusprotocol/cetus-sui-clmm-sdk'
const sqrtPriceX64 = TickMath.tickIndexToSqrtPriceX64(tickIndex)
4. Sqrt price x64 to tick index
use /src/math/tick.ts TickMath.sqrtPriceToTickIndex()
import { TickMath } from '@cetusprotocol/cetus-sui-clmm-sdk'
const tickIndex = TickMath.sqrtPriceX64ToTickIndex(sqrtPriceX64)
5. Price to sqrt price
use /src/math/tick.ts TickMath.
priceToSqrtPriceX64()
import { TickMath } from '@cetusprotocol/cetus-sui-clmm-sdk'
// decimalsA and decimalsB means the decimal of coinA and coinB
const sqrtPriceX64 = TickMath.priceToSqrtPriceX64(price, decimalsA, decimalsB)
6. Sqrt price to price
use /src/math/tick.ts TickMath.sqrtPriceX64ToPrice()
import { TickMath } from '@cetusprotocol/cetus-sui-clmm-sdk'
// decimalsA and decimalsB means the decimal of coinA and coinB
const price = TickMath.sqrtPriceX64ToPrice(sqrtPriceX64, decimalsA, decimalsB)
7. Convert the tick index from i32 to u32
In the TS SDK, for easier display, we will convert u32 to i32. If you need to call the contract directly, you can also use the method below to convert i32 to u32.
import { asUintN } from '@cetusprotocol/cetus-sui-clmm-sdk'
const tickLowerI32 = -100
const tickLowerU32 = asUintN(BigInt(tickLowerI32)).toString()
const tickUpperI32 = 100
const tickUpperU32 = asUintN(BigInt(tickUpperI32)).toString()
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