> ## Documentation Index
> Fetch the complete documentation index at: https://docs.krokoswap.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Ticks and Ranges

> How V3 discretizes prices into ticks for concentrated liquidity

# Ticks and Ranges

V3 uses a **tick** system to discretize the continuous price space. Each tick represents a specific price point, and liquidity positions are defined by a range of ticks.

## Ticks

A tick `i` maps to a price via:

$$
p(i) = 1.0001^i
$$

Each tick represents a **0.01% (1 basis point)** price change from the adjacent tick. Ticks are integers ranging from `-887272` to `887272`.

| Tick   | Price   |
| ------ | ------- |
| 0      | 1.0     |
| 1      | 1.0001  |
| 100    | 1.01005 |
| 10000  | 2.71828 |
| -10000 | 0.36788 |

## Tick Spacing

Not every tick is usable — positions must align to **tick spacing** boundaries determined by the pool's fee tier:

| Fee Tier | Tick Spacing | Price Granularity |
| -------- | ------------ | ----------------- |
| 0.01%    | 1            | Every 0.01%       |
| 0.05%    | 10           | Every 0.10%       |
| 0.3%     | 60           | Every 0.60%       |
| 1%       | 200          | Every 2.02%       |

When creating a position, `tickLower` and `tickUpper` must be multiples of the pool's tick spacing.

## sqrtPriceX96

On-chain, prices are stored as **sqrtPriceX96** — the square root of the price multiplied by 2^96:

$$
\text{sqrtPriceX96} = \sqrt{p} \times 2^{96}
$$

This encoding enables efficient fixed-point arithmetic without floating-point operations. To convert back to a human-readable price:

$$
p = \left(\frac{\text{sqrtPriceX96}}{2^{96}}\right)^2
$$

## Price Ranges

A liquidity position is defined by `[tickLower, tickUpper]`:

```mermaid theme={null}
flowchart LR
    A["tickLower"] --- B["◀ Position earns fees in this range ▶"]
    B --- C["tickUpper"]
    D(("currentTick"))

    style A fill:#f59e0b,color:#fff
    style C fill:#f59e0b,color:#fff
    style B fill:#10b981,color:#fff
    style D fill:#ef4444,color:#fff
```

### Converting Between Prices and Ticks

**Price to tick**:

$$
i = \lfloor \log_{1.0001}(p) \rfloor
$$

Then round to the nearest usable tick (multiple of tick spacing).

**Tick to price**:

$$
p = 1.0001^i
$$

### Token0 and Token1

V3 defines prices as **token1 per token0** (`price = token1/token0`). The token with the lower address is always token0.

For a KAS/USDC pool where KAS is token0:

* `price = 0.05` means 1 KAS = 0.05 USDC
* `tick ≈ -29959`

## Nearest Usable Tick

When specifying a price range, the exact tick might not align with the pool's tick spacing. Use the **nearest usable tick**:

```
nearestUsableTick = round(tick / tickSpacing) × tickSpacing
```

The API and SDK handle this conversion automatically.