Genshin Impact Primogem Calculator

How Does the Formula Work?

The calculator turns primogems, Intertwined Fates and Masterless Starglitter into a number of wishes, then counts how many more you need to reach soft pity, hard pity and the worst case on the character or weapon banner. With a daily income it also counts the days left.

Character Banner Pity

Each wish has a 0.6% base chance of a 5-star, and the 90th wish without one is guaranteed to give one; HoYoverse puts the consolidated rate, pity included, at 1.6%. Large player samples show the rate rising sharply from wish 74, which is why that point is called soft pity; HoYoverse does not publish it. A 5-star on a 50/50 is either the featured character or a standard one. If it is a standard one, the next 5-star is guaranteed to be the featured character, so getting the featured character from scratch takes at most 180 wishes.

Capturing Radiance

Since version 5.0 a lost 50/50 can still turn into the featured character. HoYoverse states a base trigger chance of 0.018% and a consolidated 55% chance that a 5-star won on a 50/50 is the featured character. After the featured character has come as the second 5-star three times in a row, the next 5-star triggers Capturing Radiance for certain. It changes neither the pity counter nor the guarantee, so the calculator's worst case stays at 180 wishes: the mechanic can only shorten the path.

Weapon Banner and Epitomized Path

The weapon banner has a 0.7% base rate, a 1.85% consolidated rate and a guaranteed 5-star on the 80th wish. Each 5-star has a 75% chance of being one of the two featured weapons. With Epitomized Path you chart one of them; since version 5.0 one Fate Point is enough, so after one 5-star that is not your weapon, the next 5-star is. That caps the chosen weapon at 160 wishes (25,600 primogems). Player records put the start of weapon soft pity at wish 63.

Earning Primogems

Daily commissions pay 10 primogems each and 20 more for finishing all four, 60 a day. The Spiral Abyss resets on the 16th of each month and floors 9 to 12 pay up to 800; the Imaginarium Theater pays up to 1,000 a season; the HoYoLAB daily check-in adds 60 a month. Blessing of the Welkin Moon costs US$4.99 and gives 300 Genesis Crystals plus 90 primogems a day for 30 days. At 60 a day the 28,800 worst case takes 480 days; at 150 a day, 192 days. Enter your own daily figure for a timeline that fits your play.

Constellations

Every extra copy of the featured character goes through the same 50/50, so each copy can take up to 180 wishes. A character at constellation 6 is seven copies: at most 1,260 wishes, or 201,600 primogems. At the published 1.6% consolidated rate a 5-star comes every 62.5 wishes on average, so the usual cost is far below the worst case, but only the worst case is a guarantee.