See also: Game modifier
The Score Multiplier is a value used to determine how much osu! should multiply the score received from each individual hit object throughout a play. By default, the Score Multiplier will be 1.00x, but this value can be changed through the use of game modifiers.
For example, if a player plays an osu! beatmap with no mods enabled, and gains a final score of 100,000, then the final score will be 100,000. However, if that same player achieved the exact same play on the exact same beatmap, with the Hard Rock mod enabled, then the final score would be 106,000 because the Hard Rock mod's Score Multiplier value is 1.06x. During a play, the score multiplier value is multiplied with the current score in real-time, although it is possible to calculate the final score after-the-fact by simply multiplying the two values together:
finalScore * scoreMultiplier.
However, if multiple mods are enabled, the score multiplier value would be the two score multiplier values of each mod, multiplies together. For example, if the Hard Rock mod and Half Time mod are enabled simultaneously in osu!, the final value would be approximately 0.32x.