### Example Circle Upgrade Cost Calculation

Source: https://revolutionidle.wiki.gg/wiki/Revolution

Demonstrates how to calculate the cost of a specific circle upgrade after one ascension, considering initial cost, cost multiplier, and ascension-based cost adjustments.

```text
Red Asc. #1 Lv10 Cost
= 100 * (1.24 ^ 100) * (1.34 ^ 10) ⵙ
= 100 * 2,198,712,860 * 18.66 ⵙ
≈ 4.1e12 ⵙ
```

--------------------------------

### Attack Circle Stats Formula

Source: https://revolutionidle.wiki.gg/wiki/Attacks

Formulas for calculating the cost of upgrading Attack Circles and their base cost for the next ascension stage.

```plaintext
1.25+(0.15×CurrentAscensionStage)
```

```plaintext
BaseCostforcurrentAscensionStage×(1.25+(0.15×CurrentAscensionStage))20
```

--------------------------------

### Circle Ascension Stats Comparison

Source: https://revolutionidle.wiki.gg/wiki/Revolution

Compares the stats of a Circle before and after its first ascension, highlighting changes in level cap, ascension power, and mult gain.

```text
| →
---
| Red Asc. #0
---
Asc. Power: x10.00 Level: 100/100 Mult Gain: x0.01
| →
---
| Red Asc. #1
---
Asc. Power: x10.00 Level: 5/110 Mult Gain: x0.11
```

--------------------------------

### Circle Progression Order

Source: https://revolutionidle.wiki.gg/wiki/Revolution

Lists the order in which Circles are unlocked and become available for purchase in the game.

```text
Red → Orange → Yellow → Green → Turquoise → Cyan → Blue → Purple → Pink → White
```

--------------------------------

### Score Income Formula (Pre-Prestige)

Source: https://revolutionidle.wiki.gg/wiki/Revolution

Provides the formula for calculating Score per second before the prestige mechanic is active. It involves the sum of all Circles' revolutions per second and the score per revolution.

```text
**ⵙ/second** = ⵙ/Revolution * [Sum of all Circles' Revolutions/second]
**ⵙ/Revolution** = ([Product of all Circles' Mults] * P.Mult)^Common Exponent
```

--------------------------------

### Damage Multiplier Formula

Source: https://revolutionidle.wiki.gg/wiki/Attacks

Formula for calculating the Damage Multiplier for Attack Circles, influenced by Ascension Power and Stage.

```plaintext
Damage Mult=CircleBaseDamage×Asc.PowerAsc.Stage
```

--------------------------------

### Display Request ID

Source: https://revolutionidle.wiki.gg/wiki/Special%3ARandom

Displays the unique identifier for a security verification request.

```text
                        
Request ID: 9e503a93cd6ef272

                    
```

--------------------------------

### Multiplier Gain Formulas After Achievement #51

Source: https://revolutionidle.wiki.gg/wiki/Achievements

After achievement #51, both the general multiplier gain and the generators' gain multiplier are affected by this formula. It continues the linear progression.

```plaintext
Mult. Gain Multiplier=1+(N×0.01)
Generators Gain Multiplier=1+(N×0.01)
```

--------------------------------

### Multiplier Gain Formulas After Achievement #201

Source: https://revolutionidle.wiki.gg/wiki/Achievements

Beyond achievement #201, the formulas for multiplier gains become more complex, affecting general multipliers, generators, dilation points, zodiac quality, and damage.

```plaintext
Mult. Gain Multiplier=1.05N×N(N20−10)
Generators Gain Multiplier=1.05N×N(N20−10)
Dilation Points Gain Multiplier=1.05N×N(N20−10)
Zodiacs Quality Multiplier=N50−2
Damage Multiplier=N50−2
```

--------------------------------

### Multiplier Gain Formula Before Achievement #51

Source: https://revolutionidle.wiki.gg/wiki/Achievements

This formula applies to the multiplier gain before reaching achievement #51. It calculates a simple linear increase based on the number of achievements (N).

```plaintext
Mult. Gain Multiplier=1+(N×0.01)
```

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