Tick

In the context of decentralized finance (DeFi) and Automated Market Makers (AMMs) like Uniswap V3, a tick is a discrete price point on a price continuum, defined by a tick index. Each tick represents a specific exchange rate between two assets in a liquidity pool, and liquidity providers (LPs) can allocate their capital to specific tick ranges, a mechanism known as concentrated liquidity. This is a fundamental shift from earlier AMM models (e.g., Uniswap V2) where liquidity was distributed uniformly across the entire price range from zero to infinity.

The system is mathematically defined. The price P at a given tick index i is calculated as P = 1.0001^i. This fixed multiplier of 1.0001 (a 0.01% increase per tick) creates a geometric progression of prices. The tick spacing—a pool parameter (e.g., 1, 10, 60, 200)—determines which ticks are usable for providing liquidity, with larger spacings reducing gas costs for swaps but decreasing granularity. When a swap moves the pool's current price across a tick boundary, it triggers the minting or burning of liquidity and the execution of any limit orders placed at that price.

For liquidity providers, ticks define the active range of their position. Capital deposited between a lower tick and an upper tick only earns fees when the market price is within that price range. This allows LPs to achieve higher capital efficiency by concentrating funds around expected price action, similar to a traditional limit order book. The tick system also enables the creation of range orders and more complex DeFi primitives like perpetuals and options, as liquidity can be programmatically deployed at precise price levels.

A tick is the smallest, discrete price interval on a price curve within an Automated Market Maker (AMM) like Uniswap V3, representing a fixed-point arithmetic unit for calculating prices and liquidity. Unlike the continuous x * y = k curve of earlier AMMs, the price space is divided into a series of ticks, each with an index corresponding to a specific price. This granular division allows liquidity providers (LPs) to concentrate their capital within specific price ranges, dramatically increasing capital efficiency for traders and enabling more sophisticated market-making strategies.

The system is defined by a tick spacing parameter, which determines how many ticks apart liquidity positions can be placed. For a pool with a tick spacing of 10, LPs can only provide liquidity at ticks with indices that are multiples of 10 (e.g., -100, -90, -80...). This creates a trade-off: smaller spacing allows for more precise concentration but increases gas costs for computation, while larger spacing reduces granularity and gas overhead. Each tick marks a boundary where the liquidity available for trading changes, as LPs' positions become active or inactive.

When a trade moves the current price across a tick boundary, the AMM's active liquidity is updated. The pool's virtual reserves are recalculated based on the combined liquidity of all positions that are active within the new price range. This mechanism ensures that swaps execute against the appropriate depth of liquidity at any given price. The tick structure also enables the precise calculation of fees earned by each LP, as fees accumulate per unit of liquidity provided within the active ticks of their position.

A tick is the smallest discrete price interval at which liquidity can be concentrated in an AMM like Uniswap V3. The tick spacing defines the multiple of these base ticks that are active for a given pool. For example, a pool with a 1% fee tier might have a tick spacing of 200, meaning liquidity can only be placed at price points that are multiples of 200 ticks apart. This parameter is fundamental because it creates a trade-off: smaller spacing allows for finer, more capital-efficient price ranges but increases gas costs due to more potential ticks; larger spacing reduces gas overhead but creates coarser, less efficient liquidity distribution.

The granularity of liquidity is directly governed by tick spacing. Each active tick corresponds to a specific price, calculated as (1.0001)^(tick index). When a liquidity provider sets a range, they select a lower tick and an upper tick that must be divisible by the pool's spacing. The space between these ticks is divided into discrete liquidity positions. This design allows liquidity to be allocated with surgical precision around expected price ranges, a stark contrast to the uniform distribution across all prices found in constant product AMMs like Uniswap V2.

From a protocol design perspective, tick spacing is a critical lever for managing system performance and capital efficiency. Protocols typically set a default spacing for each fee tier (e.g., 0.05%, 0.3%, 1%), balancing the needs of sophisticated market makers against the computational load on the network. The choice impacts how tightly liquidity aggregates around the current price, which in turn affects slippage for traders and fee revenue for liquidity providers. It is a core example of a parameter that tailors AMM behavior for specific asset pairs and volatility profiles.

In concentrated liquidity AMMs like Uniswap V3, the current price of an asset pair is not stored as a floating-point number but is instead represented by a discrete tick index. The price is calculated directly from this index using the formula price = 1.0001 ^ tick. This design ensures that price granularity is extremely fine (ticks are spaced at 0.01% intervals) while allowing all price-related calculations to be performed using efficient, gas-optimized integer math on-chain, avoiding expensive decimal operations.

The relationship is exponential: a tick is essentially the base-1.0001 logarithm of the price. For example, if the current tick is 200,000, the price is 1.0001 ^ 200,000. Conversely, to find the tick for a target price, the calculation is tick = log₁.₀₀₀₁(price). This system creates a one-to-one mapping where every possible price within the AMM's design space corresponds to a unique, signed integer tick. The sqrtPriceX96 value, a common state variable, is a fixed-point representation of the square root of this calculated price, used internally for liquidity math.

This tick-based pricing is fundamental to the concentrated liquidity model. Liquidity providers (LPs) allocate capital to specific tick ranges (e.g., from tick -100 to tick +100). The pool's active liquidity—and thus its ability to facilitate swaps—is determined by which ticks are currently crossed. When a swap moves the price, it traverses these ticks sequentially. Each time a tick boundary is crossed, the pool's active liquidity changes as positions enter or exit the active range, directly impacting the swap's execution price and slippage.