Quick answer
The probability of a five-card poker hand is the number of such hands divided by C(52, 5) = 2,598,960. A royal flush has 4 hands, odds of 1 in 649,740 and a probability of 0.000154%.
Choose a hand. The calculator returns the number of hands, probability and odds.
Related tools: Odds Ratio Calculator: Odds ratio from a 2×2 table.
How to use the Poker Hand Odds Calculator
- Choose hand: Royal flush, Straight flush (not royal), Four of a kind, Full house, Flush (not straight) and Straight (not flush) and 4 more.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Hand | Choose one: Royal flush; Straight flush (not royal); Four of a kind; Full house; Flush (not straight); Straight (not flush); Three of a kind; Two pair; … | Starts at One pair |
Formula and method
Formula
probability = number of hands ÷ C(52, 5) = ÷ 2,598,960
IEEE-754 double precision; shown to the decimals indicated.
Counts of five-card hands from a standard 52-card deck.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Hand = Royal flush.
| Result | Value |
|---|---|
| Odds | 1 in 649,740 |
| Number of hands | 4 |
| Probability | 0.000154% |
Example 2
Inputs: Hand = Straight flush (not royal).
| Result | Value |
|---|---|
| Odds | 1 in 72,193.33 |
| Number of hands | 36 |
| Probability | 0.001385% |
Example 3
Inputs: Hand = Four of a kind.
| Result | Value |
|---|---|
| Odds | 1 in 4,165 |
| Number of hands | 624 |
| Probability | 0.02401% |
The first line is the headline result (odds). Below it the poker Hand Odds Calculator lists number of hands and probability, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
The calculation
There are 4 royal flushes (one per suit). 4 ÷ 2,598,960 = 0.00000154, or 0.000154%. A straight flush including royals has 40 hands, and four of a kind 624.
Scope
The odds apply to a five-card deal with no draws or wild cards. Texas hold'em and draw poker have different probabilities. A pair occurs about 42% of the time and a flush about 0.2%.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Hand: left empty shows "Enter hand." beside that field and no result.
Choosing between the Poker Hand Odds Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Powerball Odds Calculator](/other/powerball/) | white balls matched and powerball matched? | Odds |
| [Odds Ratio Calculator](/statistics/odds-ratio-calculator/) | exposed with outcome, exposed without outcome and unexposed with outcome | Odds ratio |
| [Nether Portal Coordinates Calculator](/other/nether-portal/) | i know coordinates in the, x and z | Matching coordinates (X, Z) |
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| [K/D Ratio Calculator](/other/kd/) | kills and deaths | K/D ratio |
Background: odds and combinations
Odds in lotteries and card games rest on combinations: the number of ways to choose k items from n when order does not matter is C(n, k) = n! ÷ (k! × (n − k)!). A 6/49 lottery has C(49, 6) = 13,983,816 possible tickets, so a jackpot has odds of 1 in 13,983,816, and a five-card poker hand has C(52, 5) = 2,598,960 possibilities.
A probability is the count of favourable outcomes divided by the total, for example four of a kind has 13 × 48 = 624 hands. Past results do not change the odds of the next draw.
Assumptions and limitations
- Five cards dealt; no draws or wild cards
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for hand to confirm this.
Frequently asked questions
What are the odds of a flush?
A flush (not a straight flush) occurs in 5,108 of 2,598,960 hands, about 1 in 509.
What is the most common hand?
One pair or high card.
Do odds change with more players?
Not for your own hand.
What does the Poker Hand Odds Calculator calculate?
Odds of being dealt a five-card poker hand. It returns Odds, Number of hands and Probability.
What formula does the Poker Hand Odds Calculator use?
probability = number of hands ÷ C(52, 5) = ÷ 2,598,960. Counts of five-card hands from a standard 52-card deck.
What do I need to enter in the poker Hand Odds Calculator?
You enter Hand.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Five cards dealt; no draws or wild cards.
What is an example of a poker Hand Odds result?
With hand Royal flush, the odds is 1 in 649,740.
Where does the method come from?
The method follows: OpenStax, Algebra and Trigonometry 2e (Rice University): factorials, permutations and combinations.
Related calculators
- Odds Ratio Calculator — Odds ratio from a 2×2 table.
- K/D Ratio Calculator — Kill/death ratio.
- PPM Converter — Convert between ppm, ppb, ppt, percent and per mille.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): factorials, permutations and combinations
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.