Price Tick Conversions

The price tick conversion utilities provide functions for converting between Price objects and ticks in Uniswap V3.

Import

import { tickToPrice, priceToClosestTick } from '@uniswap/v3-sdk'

Functions

tickToPrice

Returns a Price object corresponding to the input tick and the base/quote tokens.

function tickToPrice(baseToken: Token, quoteToken: Token, tick: number): Price<Token, Token>

Parameters

Parameter	Type	Description
`baseToken`	`Token`	The base token of the price
`quoteToken`	`Token`	The quote token of the price
`tick`	`number`	The tick for which to return the price

Returns

Returns a Price<Token, Token> object representing the price at the given tick.

Example

import { tickToPrice } from '@uniswap/v3-sdk'
import { Token } from '@uniswap/sdk-core'
 
const USDC = new Token(1, '0xA0b86991c6218b36c1d19D4a2e9Eb0cE3606eB48', 6, 'USDC')
const WETH = new Token(1, '0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2', 18, 'WETH')
 
// Get price at tick 0 (approximately 1:1)
const priceAtTick0 = tickToPrice(USDC, WETH, 0)
console.log(priceAtTick0.toSignificant(6)) // "1"
 
// Get price at tick 100
const priceAtTick100 = tickToPrice(USDC, WETH, 100)
console.log(priceAtTick100.toSignificant(6)) // "1.01005"
 
// Get price at tick -100
const priceAtTickMinus100 = tickToPrice(USDC, WETH, -100)
console.log(priceAtTickMinus100.toSignificant(6)) // "0.990049"

priceToClosestTick

Returns the first tick for which the given price is greater than or equal to the tick price.

function priceToClosestTick(price: Price<Token, Token>): number

Parameters

Parameter	Type	Description
`price`	`Price<Token, Token>`	The price for which to return the closest tick

Returns

Returns the closest tick (number) to the given price.

Example

import { priceToClosestTick, tickToPrice } from '@uniswap/v3-sdk'
import { Price, Token } from '@uniswap/sdk-core'
 
const USDC = new Token(1, '0xA0b86991c6218b36c1d19D4a2e9Eb0cE3606eB48', 6, 'USDC')
const WETH = new Token(1, '0xC02aaA39b223FE8D0A0e5C4F27eAD9083C756Cc2', 18, 'WETH')
 
// Create a price (1 USDC = 0.0005 WETH, meaning 1 ETH = 2000 USDC)
const price = new Price(USDC, WETH, 2000, 1) // quoteAmount / baseAmount
 
const tick = priceToClosestTick(price)
console.log(tick)

Token Order Matters

The order of tokens affects the interpretation of the price and tick:

import { tickToPrice } from '@uniswap/v3-sdk'
 
// USDC as base, WETH as quote: "How much WETH per USDC?"
const priceUsdcBase = tickToPrice(USDC, WETH, 100)
console.log(`1 USDC = ${priceUsdcBase.toSignificant(6)} WETH`)
 
// WETH as base, USDC as quote: "How much USDC per WETH?"
const priceWethBase = tickToPrice(WETH, USDC, 100)
console.log(`1 WETH = ${priceWethBase.toSignificant(6)} USDC`)

Use Cases

Setting Position Price Range

import { tickToPrice, priceToClosestTick } from '@uniswap/v3-sdk'
import { Price, Token } from '@uniswap/sdk-core'
 
// Define desired price range
const lowerPrice = new Price(WETH, USDC, 1, 1800) // 1 ETH = 1800 USDC
const upperPrice = new Price(WETH, USDC, 1, 2200) // 1 ETH = 2200 USDC
 
// Convert to ticks
const tickLower = priceToClosestTick(lowerPrice)
const tickUpper = priceToClosestTick(upperPrice)
 
// Round to valid tick spacing (e.g., 60 for 0.3% fee tier)
const tickSpacing = 60
const tickLowerRounded = Math.floor(tickLower / tickSpacing) * tickSpacing
const tickUpperRounded = Math.ceil(tickUpper / tickSpacing) * tickSpacing
 
// Get the actual prices for the rounded ticks
const actualLowerPrice = tickToPrice(WETH, USDC, tickLowerRounded)
const actualUpperPrice = tickToPrice(WETH, USDC, tickUpperRounded)
 
console.log(`Lower: ${actualLowerPrice.toSignificant(6)} USDC/ETH`)
console.log(`Upper: ${actualUpperPrice.toSignificant(6)} USDC/ETH`)

Displaying Current Pool Price

import { tickToPrice } from '@uniswap/v3-sdk'
 
// Get the current tick from pool state
const currentTick = pool.tickCurrent
 
// Convert to human-readable price
const currentPrice = tickToPrice(pool.token1, pool.token0, currentTick)
console.log(`Current price: ${currentPrice.toSignificant(6)}`)

Creating a Price from Amounts

import { priceToClosestTick } from '@uniswap/v3-sdk'
import { Price, Token } from '@uniswap/sdk-core'
 
// If 1000 USDC trades for 0.5 WETH
const price = new Price(
  USDC,
  WETH,
  1000n * 10n ** 6n,    // 1000 USDC in smallest units
  5n * 10n ** 17n       // 0.5 WETH in smallest units
)
 
const tick = priceToClosestTick(price)

Price Formula

The relationship between tick and price is:

price = 1.0001^tick

For the Q64.96 sqrt price format:

sqrtPriceX96 = sqrt(1.0001^tick) * 2^96

Handling Token Decimals

The Price class automatically handles decimal differences between tokens:

import { tickToPrice } from '@uniswap/v3-sdk'
 
const USDC = new Token(1, '0x...', 6, 'USDC')   // 6 decimals
const WETH = new Token(1, '0x...', 18, 'WETH') // 18 decimals
 
// The price is automatically adjusted for decimals
const price = tickToPrice(USDC, WETH, 0)
 
// Display in human-readable format
console.log(price.toSignificant(6))      // Decimal-adjusted
console.log(price.toFixed(18))           // Full precision

Precision Considerations

Due to the discrete nature of ticks, there may be small rounding errors:

import { tickToPrice, priceToClosestTick } from '@uniswap/v3-sdk'
 
const originalTick = 12345
const price = tickToPrice(token0, token1, originalTick)
const recoveredTick = priceToClosestTick(price)
 
// recoveredTick should equal originalTick, but verify
console.log(originalTick === recoveredTick) // true (in most cases)

The priceToClosestTick function returns the floor tick, so there may be edge cases where the exact tick differs by 1.