Powerball Odds Calculator
Use this calculator to determine the probability of winning various Powerball prize tiers based on the number of white balls and the Powerball you match.
.powerball-calculator-container {
font-family: 'Arial', sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
box-shadow: 0 2px 4px rgba(0,0,0,0.1);
}
.powerball-calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
}
.powerball-calculator-container p {
color: #555;
margin-bottom: 15px;
line-height: 1.6;
}
.powerball-calculator-form .form-group {
margin-bottom: 15px;
}
.powerball-calculator-form label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #444;
}
.powerball-input {
width: 100%;
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
font-size: 16px;
}
.radio-group {
display: flex;
gap: 15px;
align-items: center;
}
.radio-group input[type="radio"] {
margin-right: 5px;
}
.powerball-button {
background-color: #e74c3c; /* Powerball red */
color: white;
padding: 12px 20px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 18px;
width: 100%;
box-sizing: border-box;
transition: background-color 0.3s ease;
}
.powerball-button:hover {
background-color: #c0392b;
}
.powerball-result {
margin-top: 20px;
padding: 15px;
border: 1px solid #dcdcdc;
border-radius: 4px;
background-color: #eef;
color: #333;
font-size: 1.1em;
line-height: 1.6;
}
.powerball-result strong {
color: #e74c3c;
}
.powerball-result .prize-info {
font-style: italic;
color: #666;
margin-top: 5px;
}
// Function to calculate combinations (nCr)
function nCr(n, r) {
if (r n) return 0;
if (r === 0 || r === n) return 1;
if (r > n / 2) r = n – r; // Optimization
var res = 1;
for (var i = 1; i <= r; i++) {
res = res * (n – i + 1) / i;
}
return res;
}
function calculatePowerballOdds() {
var whiteBallsMatched = parseInt(document.getElementById('whiteBallsMatched').value);
var powerballMatched = document.getElementById('powerballMatchedYes').checked;
// Constants for Powerball
var TOTAL_WHITE_BALLS = 69;
var WHITE_BALLS_DRAWN = 5;
var TOTAL_POWERBALLS = 26;
var POWERBALLS_DRAWN = 1;
// Calculate total possible combinations
var totalWhiteCombinations = nCr(TOTAL_WHITE_BALLS, WHITE_BALLS_DRAWN);
var totalPowerballCombinations = nCr(TOTAL_POWERBALLS, POWERBALLS_DRAWN);
var totalOverallCombinations = totalWhiteCombinations * totalPowerballCombinations;
// Calculate favorable combinations for white balls
var waysToMatchWhite = nCr(WHITE_BALLS_DRAWN, whiteBallsMatched);
var waysToPickIncorrectWhite = nCr(TOTAL_WHITE_BALLS – WHITE_BALLS_DRAWN, WHITE_BALLS_DRAWN – whiteBallsMatched);
var favorableWhiteCombinations = waysToMatchWhite * waysToPickIncorrectWhite;
// Calculate favorable combinations for Powerball
var favorablePowerballCombinations = powerballMatched ? nCr(POWERBALLS_DRAWN, 1) : nCr(TOTAL_POWERBALLS – POWERBALLS_DRAWN, 1);
// Calculate overall favorable combinations
var favorableOverallCombinations = favorableWhiteCombinations * favorablePowerballCombinations;
var resultDiv = document.getElementById('powerballResult');
if (favorableOverallCombinations === 0) {
resultDiv.innerHTML = "There are no combinations that match your criteria. This scenario is impossible.";
return;
}
var odds = totalOverallCombinations / favorableOverallCombinations;
var probability = (favorableOverallCombinations / totalOverallCombinations) * 100;
var prizeInfo = "";
var prizeKey = whiteBallsMatched + "_" + (powerballMatched ? "1" : "0");
// Define prize tiers and their associated prizes
var prizeTiers = {
"5_1": "Grand Prize (Jackpot)",
"5_0": "$1,000,000",
"4_1": "$50,000",
"4_0": "$100",
"3_1": "$100",
"3_0": "$7",
"2_1": "$7",
"1_1": "$4",
"0_1": "$4"
};
if (prizeTiers[prizeKey]) {
prizeInfo = "This combination typically wins:
" + prizeTiers[prizeKey] + "";
} else {
prizeInfo = "This combination is not a winning prize tier.";
}
resultDiv.innerHTML =
"Your odds of matching
" + whiteBallsMatched + " white ball(s) and " +
(powerballMatched ? "the
Powerball" : "
NOT the Powerball") +
" are approximately
1 in " + odds.toLocaleString(undefined, { maximumFractionDigits: 2 }) + "." +
"This represents a probability of
" + probability.toFixed(8) + "%." +
prizeInfo;
}
// Calculate on page load with default values
document.addEventListener('DOMContentLoaded', function() {
calculatePowerballOdds();
});
Understanding Powerball Odds
Powerball is a popular multi-state lottery game in the United States. To play, participants choose five numbers from a set of 69 white balls and one number from a set of 26 red Powerballs. To win the jackpot, a player must match all five white balls and the red Powerball.
How the Calculator Works
This calculator uses principles of combinatorics to determine the exact odds for any specific matching scenario. Here's a breakdown:
- White Balls: There are 69 white balls, and 5 are drawn. The number of ways to choose 5 white balls from 69 is calculated using the combination formula C(n, k) = n! / (k! * (n-k)!).
- Powerball: There are 26 red Powerballs, and 1 is drawn. The number of ways to choose 1 Powerball from 26 is simply 26.
- Total Combinations: The total number of unique Powerball tickets possible is the product of the white ball combinations and the Powerball combinations. This results in a staggering 292,201,338 unique combinations.
- Favorable Combinations: Based on your input (how many white balls you match and whether you match the Powerball), the calculator determines how many of these total combinations would result in that specific outcome.
- Odds Calculation: The odds are then calculated by dividing the total possible combinations by the number of favorable combinations.
Powerball Prize Tiers and Example Odds
Here are the odds for the main Powerball prize tiers:
- Grand Prize (5 White + Powerball): 1 in 292,201,338
- $1,000,000 (5 White + No Powerball): 1 in 11,688,053.52
- $50,000 (4 White + Powerball): 1 in 913,129.18
- $100 (4 White + No Powerball): 1 in 36,525.17
- $100 (3 White + Powerball): 1 in 14,494.11
- $7 (3 White + No Powerball): 1 in 579.76
- $7 (2 White + Powerball): 1 in 701.19
- $4 (1 White + Powerball): 1 in 91.98
- $4 (0 White + Powerball): 1 in 38.32
As you can see, the odds of winning the jackpot are extremely low, highlighting that Powerball is a game of pure chance. Even for smaller prizes, the odds can be quite high.