HSR Summon Calculator

Accurately estimate your chances of acquiring desired Light Cones and Eidolons in Honkai: Star Rail. Input your current summon data and see your probabilities!

Honkai: Star Rail Summon Probability Calculator

What is an HSR Summon Calculator?

An HSR Summon Calculator, short for Honkai: Star Rail Summon Calculator, is a specialized tool designed to help players understand and quantify their chances of obtaining specific characters, Light Cones, or other valuable items from the game’s gacha or “warp” system. Unlike generic probability tools, this calculator is tailored to the unique mechanics of Honkai: Star Rail, incorporating elements like guaranteed pity, banner types, and the soft pity system.

Who Should Use It:

• New Players: To grasp the gacha system’s intricacies and plan their resource (Special Star Rail Passes, Stellar Jade) spending.
• Strategic Spenders: Players aiming for specific limited characters or Light Cones who want to optimize their pulls and understand the potential cost.
• Whales and F2P alike: Anyone curious about their odds, whether they spend money or rely solely on in-game rewards, to set realistic expectations.
• Players Experiencing Bad Luck: To get a clearer picture of their situation and potentially prepare for longer pulls.

Common Misconceptions:

• “It’s just random luck”: While randomness is involved, HSR’s pity system significantly increases the *guaranteed* chance of obtaining a 5-star item within a set number of pulls, making it more predictable than pure chance.
• “My next pull is guaranteed”: This is only true if you have lost the 50/50 on a limited banner and have not yet received a 5-star on the current pity counter. The calculator helps track this.
• “Soft pity starts exactly at pull 75”: The exact mechanics of soft pity are not officially detailed but are widely believed to begin increasing probability significantly after pull 74, rather than a hard switch. The calculator uses common approximations.
• “Pulls reset across banners”: Pity counters are specific to each banner type (Standard, Limited Character, Limited Light Cone). Pulls on one do not affect the pity on another, except for the Standard banner’s pity count potentially carrying over to the next Standard banner if not triggered.

HSR Summon Calculator Formula and Mathematical Explanation

The HSR Summon Calculator operates by calculating probabilities based on the game’s established pity mechanics. Here’s a breakdown of the core logic:

Base Probabilities

The fundamental probability of pulling a 5-star item on any given pull (before pity kicks in) is generally accepted to be 0.6%. The probability of pulling a 4-star item is approximately 5.1%, and 3-star items (from Warp material) make up the rest.

The Pity System

Honkai: Star Rail employs a pity system to ensure players eventually receive high-rarity items. This system has two main components:

• Hard Pity: Guarantees a 5-star item by the 90th pull on Standard and Character Warps, and the 80th pull on Light Cone Warps.
• Soft Pity: A widely observed phenomenon where the probability of pulling a 5-star begins to increase significantly after a certain number of pulls (commonly estimated around the 74th pull for Character/Standard banners and 65th for Light Cone banners). The calculator models this increasing probability.

Calculating Chance for Next 5-Star

This calculation considers the number of pulls since the last 5-star and the soft/hard pity thresholds.

Let P_base be the base 5-star probability (0.006).
Let N be the number of pulls since the last 5-star (`currentPulls`).
Let P_soft_start be the pull number where soft pity begins (e.g., 74 for Character/Standard, 65 for LC).
Let P_hard_limit be the pull number for hard pity (90 for Character/Standard, 80 for LC).

For N < P_soft_start: The probability is approximately P_base.

For P_soft_start ≤ N < P_hard_limit: The probability increases incrementally for each pull. A common approximation models this as a linear increase, or more complex curves, to reach 100% at P_hard_limit. The calculator uses a simplified model where probability increases slightly per pull.

For N = P_hard_limit: The probability is 100%.

Calculating Chance for Desired 5-Star

This is more complex and depends on the banner type and the `guaranteedPity` setting.

• Standard/LC Banner: There’s a 50% chance the next 5-star is the featured Light Cone (on the LC banner) or a specific standard character. On the Standard Banner, the odds are split among the standard pool.
• Limited Character Banner:
  • If guaranteedPity is ‘true’: The next 5-star is guaranteed to be the featured character. The probability is simply the calculated “Chance for Next 5-Star”.
  • If guaranteedPity is ‘false’: There’s a 50% chance the next 5-star is the featured character, and a 50% chance it’s a standard 5-star character. The probability is (Chance for Next 5-Star) * 0.5.

The calculator also factors in the `bannerTargetPulls`. The probability of getting the desired item *within* this target is calculated by summing the probabilities of getting it on each pull from 1 up to `bannerTargetPulls`. This involves complex summation of probabilities considering pity progression.

Average Pulls for Desired 5-Star

This estimates the expected number of pulls needed. It’s roughly the inverse of the probability of obtaining the desired item on any given pull, but refined using the pity system’s cumulative probabilities. It’s often calculated using simulations or complex probability formulas that account for the increasing odds.

Average Pulls for Any 5-Star

This is the expected number of pulls to get *any* 5-star item, considering the pity system. It’s generally around 75-80 pulls for character/standard banners and slightly lower for LC banners, accounting for soft pity.

Variable Explanations

Variable	Meaning	Unit	Typical Range
P_base	Base probability of pulling a 5-star item.	Probability (Decimal)	0.006
N (`currentPulls`)	Number of pulls made since the last 5-star item.	Pulls	0 – 90 (or 80 for LC)
P_soft_start	The pull number where the probability of pulling a 5-star begins to significantly increase.	Pull Number	~74 (Character/Standard), ~65 (LC)
P_hard_limit	The maximum number of pulls before a 5-star item is guaranteed.	Pull Number	90 (Character/Standard), 80 (LC)
guaranteedPity	Indicates if the next 5-star is guaranteed to be the featured item on a limited banner.	Boolean (True/False)	True, False
bannerPulls (`bannerPulls`)	Total number of pulls made on the current specific banner.	Pips (Special Star Rail Passes)	0+
bannerTargetPulls (`bannerTargetPulls`)	The maximum number of Pips the user is willing to spend for a desired item.	Pips (Special Star Rail Passes)	0+
Desired 5-Star Rate	Probability of obtaining the specific featured item (character/LC) on a limited banner.	Percentage (%)	Depends on guaranteedPity (50% or 100%)

Practical Examples (Real-World Use Cases)

Example 1: Aiming for a Limited Character (With Guarantee)

Scenario: A player wants the limited character “Dr. Ratio” on his event banner. They have pulled 50 times on this banner already and just received a standard 5-star character (meaning their next 5-star is guaranteed to be Dr. Ratio). They are willing to spend up to 120 Pips total on this banner.

Inputs:

• Banner Type: Limited Character Warp
• Guaranteed Pity: Yes
• Pulls Since Last 5-Star: 50 (assuming the standard was pulled at pity 50)
• Total Pips Used This Banner: 50
• Target Pips for Desired Item: 120

Calculator Outputs (Illustrative):

• Primary Result: ~77.78% (Chance to get Dr. Ratio within the remaining 70 pulls, i.e., hitting 120 total)
• Chance for next 5-Star: ~12.3% (at pull 51, considering soft pity starts around 74)
• Chance for Desired 5-Star (within target): ~77.78%
• Avg. Pulls for Desired 5-Star: ~21 pulls (remaining needed)
• Avg. Pulls for Any 5-Star: ~15 pulls (remaining needed)

Interpretation: Even though their next 5-star is guaranteed, hitting exactly the 120 Pip mark isn’t certain. The calculator shows a high probability (~77.78%) of getting Dr. Ratio within their target of 120 Pips (meaning within the next 70 pulls). They are likely to get him, but there’s still a chance they might need more than 120 Pips.

Example 2: Pulling on Standard Banner (No Guarantee)

Scenario: A player is on the Standard Warp banner. They just received a 5-star character 10 pulls ago. They want to know their general odds of getting *any* 5-star within their next 30 pulls.

Inputs:

• Banner Type: Standard Warp
• Guaranteed Pity: No
• Pulls Since Last 5-Star: 10
• Total Pips Used This Banner: 10 (on this specific pity cycle)
• Target Pips for Desired Item: 30

Calculator Outputs (Illustrative):

• Primary Result: ~27.5% (Chance to get *any* 5-star within the next 30 pulls)
• Chance for next 5-Star: ~0.6% (at pull 11, base rate)
• Chance for Desired 5-Star (within target): ~27.5% (since it’s any 5-star)
• Avg. Pulls for Desired 5-Star: ~109 pulls (total expected for *any* 5-star)
• Avg. Pulls for Any 5-Star: ~78 pulls (total expected for *any* 5-star)

Interpretation: With only 10 pulls done since the last 5-star, the odds are still very low (~0.6% per pull, summing up to ~27.5% over 30 pulls). The average expected pulls for a 5-star is around 78. This player is unlikely to hit pity within their 30-pull target but has a moderate chance.

How to Use This HSR Summon Calculator

Using the HSR Summon Calculator is straightforward. Follow these steps to get accurate probability estimates:

Step-by-Step Instructions:

1. Select Banner Type: Choose the correct banner from the dropdown: “Standard Warp”, “Limited Character Warp”, or “Limited Light Cone Warp”. This is crucial as pity mechanics differ.
2. Set Guaranteed Pity: If you are on a Limited Character or Light Cone banner and have *not* received a 5-star item yet on this specific banner’s pity counter, select “No”. If you have received a standard 5-star on a character banner, or the featured 5-star on a Light Cone banner, and are now pulling for the *next* limited character/LC, select “Yes”.
3. Input Pulls Since Last 5-Star: Enter the number of pulls you’ve made on the *current banner’s pity counter* since you last acquired a 5-star item. This is the most critical input for determining current odds. Be honest!
4. Enter Total Pips Used This Banner: Input the total number of Special Star Rail Passes (Pips) you have spent on this specific banner. This helps contextualize your spending against the target.
5. Set Target Pips: Specify the maximum number of Pips you are willing to spend to get your desired item. This helps calculate the probability of success within your budget.
6. Click “Calculate Probabilities”: The calculator will process your inputs and display the results.

How to Read Results:

• Primary Result (Highlighted): This is the main probability – typically the chance of acquiring your desired item within your specified target pulls. A higher percentage means a greater likelihood.
• Chance for Next 5-Star: The immediate probability of getting *any* 5-star item on your very next pull, considering your current pity progress and soft pity.
• Chance for Desired 5-Star (within target): The calculated probability that you will obtain the specific featured item (character or Light Cone) before you reach your `bannerTargetPulls`.
• Avg. Pulls for Desired 5-Star: An estimation of how many more pulls you might *expect* to make to get the desired item, based on average luck and the pity system.
• Avg. Pulls for Any 5-Star: The average number of pulls needed to get *any* 5-star item on this banner type, considering the pity system.

Decision-Making Guidance:

Use these results to inform your pulling strategy. If the “Chance for Desired 5-Star (within target)” is low, you might consider saving more Pips or waiting for a future banner. If the average pulls are high, be prepared for potentially significant Stellar Jade or real-money expenditure. Remember, these are probabilities; actual results can vary.

Key Factors That Affect HSR Summon Results

Several elements influence your success and probabilities when pulling in Honkai: Star Rail. Understanding these can help you manage expectations and resources more effectively:

1. Pity System Mechanics:

   This is the most significant factor. The guaranteed 5-star at hard pity (90/80 pulls) and the increasing odds during soft pity (around 74/65 pulls) drastically alter probabilities compared to a flat rate. The calculator heavily relies on modeling this.

2. Banner Type:

   Limited Character banners have a 50% chance of the featured item if you haven’t triggered the guarantee. Limited Light Cone banners also have a 50% chance for the featured LC. Standard banners offer a pool of permanent 5-stars with fixed odds for each. This directly impacts the “Desired 5-Star Rate”.

3. Current Pity Count (`currentPulls`):

   The number of pulls since your last 5-star is the primary driver of your *current* probability. Being at pull 1 gives you base odds, while being at pull 80 on a character banner significantly boosts your chances.

4. Resource Management (Stellar Jade & Passes):

   Your available currency directly limits how many pulls you can perform. A large stockpile allows you to reach hard pity if necessary, while limited resources mean you must rely more on favorable odds within fewer pulls. This relates to the `bannerTargetPulls` input.

5. Player Goals & Budget (`bannerTargetPulls`):

   Are you aiming for a specific character’s Eidolon, or just the first copy? Are you a Free-to-Play player saving for months, or a spender willing to go deep? Your target and willingness to spend directly influence how you interpret the calculated probabilities and risks.

6. “Bad Luck” Streaks:

   While the average pulls are predictable, individual sessions can deviate. You might get lucky and pull a 5-star early, or unlucky and hit hard pity multiple times in a row. The calculator provides averages and probabilities, not guarantees.

7. Game Updates & New Banners:

   The introduction of new characters, Light Cones, and potential changes to banner mechanics (though unlikely) can affect long-term pulling strategies and the perceived value of existing items.

Frequently Asked Questions (FAQ)

Q1: Does pity carry over between different banners?

No, pity counters are specific to each banner type. Your progress on a Limited Character banner does not affect your pity on the Standard banner or a Limited Light Cone banner, and vice-versa. However, if you don’t hit pity on a Limited banner, the number of pulls made does carry over to the *next* banner of the same type (e.g., Limited Character pity carries to the next Limited Character banner).

Q2: What exactly is “soft pity” in HSR?

Soft pity refers to the period before hard pity where the probability of pulling a 5-star item increases significantly with each subsequent pull. While not officially confirmed with exact numbers, community data suggests it starts around the 74th pull for Character/Standard banners and the 65th for Light Cone banners, gradually increasing the odds until the guaranteed pull at 90 (or 80 for LC).

Q3: How is the “Desired 5-Star” probability calculated on Limited banners?

If `guaranteedPity` is ‘Yes’, the probability is 100% for the next 5-star pull. If `guaranteedPity` is ‘No’, there’s a 50% chance the next 5-star will be the featured item. The calculator multiplies the “Chance for Next 5-Star” by this 50% factor when `guaranteedPity` is ‘No’.

Q4: Does pulling a 4-star item reset my 5-star pity?

No, pulling a 4-star item does not reset your 5-star pity counter. The pity counter only resets once you acquire a 5-star item.

Q5: Can I use this calculator for 4-star items?

This calculator primarily focuses on the probabilities and pity system for 5-star items, as they are the most significant concern for players. While 4-star rates exist (around 5.1% base, with a separate pity at 10 pulls), calculating specific desired 4-star outcomes is more complex due to them sharing pity with other 4-stars and having their own guaranteed pity.

Q6: What are “Pips” in HSR?

“Pips” is informal community slang for Special Star Rail Passes, the premium currency used for Warps (summons) on event banners. Each Pip allows for one Warp.

Q7: What happens if I pull a Standard 5-star on a Limited Character Banner when I didn’t have the guarantee?

If you pull a Standard 5-star character while `guaranteedPity` was ‘No’, your next 5-star pull on that *same Limited Character banner* will be guaranteed to be the featured character. Your pity counter resets to 0 for the next 5-star, but the “guarantee” status is now active.

Q8: How accurate are the “Average Pulls” calculations?

The “Average Pulls” are estimations based on statistical models of the HSR pity system. They represent the expected number of pulls over many simulations. Your actual experience may vary significantly due to the inherent randomness of the gacha.

Q9: Can I calculate the probability of getting a specific Eidolon?

This calculator focuses on the probability of getting the *first copy* of a featured 5-star item. Calculating the probability for higher Eidolon levels (E2, E4, E6) requires multiplying the probability of getting the first copy by subsequent probabilities, considering you’d need to win the 50/50 again (if not guaranteed) or hit pity multiple times, making it exponentially more difficult.

Q10: My calculated probability is very low. What should I do?

Low probability means you are likely early in your pity cycle or didn’t have the guarantee active. It suggests you may need to save more Stellar Jade/Pips to reach the higher pity thresholds if you are determined to get the item. Consider if the target item is essential or if saving for a future banner might be more efficient based on your resources.

Related Tools and Resources

• Honkai Star Rail Damage CalculatorAnalyze your character’s damage output potential.
• HSR Character Tier ListDiscover the best characters in the current meta.
• HSR Light Cone RankingFind the top Light Cones for each path.
• Stellar Jade Farming GuideMaximize your free currency gains.
• HSR Relic Optimization GuideTips for farming and rolling the best relics.
• Beginner’s Guide to Honkai: Star RailEssential tips for new players.

Summon Probability Distribution