What Is a Probability Calculator?
A probability calculator is a free online tool that computes the likelihood of one or more events occurring. Our calculator covers 11 modes — single event theoretical probability, multiple events (2 or 3), conditional probability, binomial probability, normal distribution and z-score probability, implied probability from betting odds, dice roll probability, coin flip probability, poker hand probability, and pregnancy probability including miscarriage probability calculator and labor probability by week. Every result shows the formula used and step-by-step working so you understand exactly how the probability was calculated.
Probability calculator — poker hands, card games, dice rolls, coin flips, and sports betting odds
How to Use a Probability Calculator
1
Identify your probability typeIs it a single event (rolling a die), multiple events (two dice), conditional (given some information), binomial (repeated trials), or a special case like z-score, dice, coin, poker, or pregnancy probability?
2
Select the matching modeClick the correct tab at the top of the calculator. Each mode shows a description and the right input fields for that probability type.
3
Enter your valuesType in the numbers — favorable outcomes, total outcomes, probability per trial, z-score, betting odds, gestational week, or other relevant values. All fields are labeled clearly.
4
Click Calculate and read resultsGet probability as fraction, decimal, and percentage instantly. The probability meter shows where your result sits on the 0–1 scale, and the step-by-step section explains the full working.
How to Calculate Probability on a Calculator
The basic formula for theoretical probability is: P = favorable outcomes / total outcomes. This is used when all outcomes are equally likely. For more complex situations, different formulas apply.
| Problem Type | Formula | Example |
|---|
| Single event | P = F / T | Rolling a 6: 1/6 = 16.7% |
| A and B (independent) | P(A) × P(B) | Two heads: 0.5 × 0.5 = 25% |
| A or B | P(A) + P(B) - P(A and B) | King or heart: 30.8% |
| 3 events all occurring | P(A) × P(B) × P(C) | Three sixes: (1/6)³ = 0.46% |
| Conditional P(A|B) | P(A and B) / P(B) | King given face card: 33.3% |
| Binomial | C(n,k) × p^k × (1-p)^(n-k) | 3 heads in 5 flips: 31.25% |
| Complement | 1 - P(A) | Not rolling a 6: 1 - 1/6 = 83.3% |
Dice Probability Calculator
Our dice roll probability calculator supports D4, D6, D8, D10, D12, D20, and D100 dice with up to 10 dice. For a single die with n sides, the probability of rolling any specific number is 1/n. For multiple dice, the exact sum probability is calculated by counting all combinations that add up to the target value.
Dice probability examples
P(rolling at least 5 on D6) = 2/6 = 33.3% • P(sum = 7 with 2D6) = 6/36 = 16.7% • P(rolling a 20 on D20) = 1/20 = 5%
Coin Flip Probability Calculator
The coin flip probability calculator uses the binomial formula with p = 0.5. For exactly k heads in n flips: P = C(n,k) × 0.5^n. For a streak of k heads in a row: P = (0.5)^k. The law of large numbers ensures that over many flips, the observed ratio approaches 50%.
Coin flip probability examples
Exactly 5 heads in 10 flips: 24.6% • At least 7 heads in 10 flips: 17.2% • 5 heads in a row: (0.5)^5 = 3.125%
Binomial Probability Calculator
The binomial distribution probability calculator handles any repeated experiment with two outcomes (success/failure). Enter n (trials), k (successes), and p (probability per trial). Choose exactly k, at most k, or at least k successes.
Binomial example — product quality
A factory has 5% defect rate. What is the probability of finding exactly 2 defects in a batch of 20? n=20, k=2, p=0.05 → P = C(20,2) × 0.05² × 0.95¹⁸ = 189 × 0.0025 × 0.3972 = 18.79%
Normal Distribution and Z-Score Probability Calculator
The z-score probability calculator (also called the normal distribution probability calculator) finds the area under the standard normal curve. A z-score tells you how many standard deviations from the mean a value lies. Enter your z-score and choose left tail P(X < z), right tail P(X > z), two-tailed P(|X| > z), or the area between ±z.
Z-score examples
z = 1.96: Left tail = 97.5%, Right tail = 2.5% (used for 95% confidence intervals) • z = 2.576: Right tail = 0.5% (used for 99% CI) • z = 0: Left tail = 50% (median equals mean)
Implied Probability and Odds to Probability Calculator
The implied probability calculator converts betting odds into the probability that the bookmaker is pricing into each outcome. This is essential for value betting — when your calculated probability exceeds the implied probability, there may be a positive expected value.
| Odds Format | Example | Formula | Implied Prob |
|---|
| American (favorite) | -110 | 110 / (110+100) | 52.38% |
| American (underdog) | +150 | 100 / (150+100) | 40.00% |
| Decimal | 2.50 | 1 / 2.50 | 40.00% |
| Fractional | 3/2 | 2 / (3+2) | 40.00% |
Probability calculator for statistics, medicine, sports betting, science, and everyday decisions
Poker Probability Calculator
Our poker probability calculator shows the exact probability of being dealt each poker hand from a standard 52-card deck. The total number of 5-card hands is C(52,5) = 2,598,960. Probabilities range from the royal flush (1 in 649,740) to a high card hand (50.12%). Pre-flop probabilities are also included for pocket pairs, suited connectors, and specific starting hands like AK.
Pregnancy Probability Calculator
Our pregnancy probability calculator provides three statistical measures based on published population data:
- Conception probability: Estimated chance of conceiving per cycle, adjusted for age. Fertility declines progressively after 30 and more significantly after 35.
- Miscarriage probability: The risk of pregnancy loss by gestational week. Risk is highest in weeks 5–6 and decreases significantly after week 10 when a heartbeat is detected.
- Labor probability by week: The probability of spontaneous labor occurring at or before a given gestational week. Most term pregnancies deliver between weeks 39–41.
Important: Pregnancy probability data is based on population averages and published research. These figures are for educational and informational purposes only. Always consult your OB-GYN, midwife, or healthcare provider for personalized medical advice and risk assessment.
Probability Calculator for 3 Events
Our probability calculator for 3 events calculates all three events occurring simultaneously (A AND B AND C), at least one occurring (A OR B OR C), and none occurring. For independent events: P(A and B and C) = P(A) × P(B) × P(C). For "at least one": P(at least one) = 1 – P(none) = 1 – (1-P(A)) × (1-P(B)) × (1-P(C)).
3-event example
P(A)=0.5, P(B)=0.3, P(C)=0.4 → P(all three) = 0.5 × 0.3 × 0.4 = 6% • P(at least one) = 1 – 0.5 × 0.7 × 0.6 = 1 – 0.21 = 79%
How to find probability on a calculator: Match your question to the right mode. For equally-likely outcomes use Single Event. For two events use AND/OR mode. For given information use Conditional. For repeated trials use Binomial. For bell curve statistics use Z-Score. For betting lines use Implied Odds. The calculator shows you the formula and every step of the calculation.
