Coin Toss Probability Calculator
Calculate the probability of getting exactly k heads in n fair coin tosses.
About Coin Toss Probability Calculator
Coin toss probability is a direct application of the binomial distribution. With n independent tosses each having probability p of heads, the probability of exactly k heads is C(n,k) × p^k × (1−p)^(n−k).
Formula
P(k heads in n tosses) = C(n,k) × p^k × (1−p)^(n−k)
- n
- Number of tosses
- k
- Desired heads
- p
- Probability of heads per toss
Worked example
With the default values below, Coin Toss Probability Calculator returns P(exactly k heads) of 0.24609375. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Number of Tossesaccepts 1–100
- 10
- Desired Headsminimum 0
- 5
- P(Heads) per tossaccepts 0–1
- 0.5
Results
- P(exactly k heads)
- 0.24609375
- P(≥ k heads)
- 0.62304688
- P(≤ k heads)
- 0.62304688
Step by step
- 1Values used
- 2Formula applied
- 3P(exactly k heads)= 0.24609375
- 4P(≥ k heads)= 0.62304688
- 5P(≤ k heads)= 0.62304688
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the probability of getting 5 heads in 10 fair coin flips?
C(10,5) × 0.5^10 = 252/1024 ≈ 0.2461 or about 24.6%.
Is each toss truly independent?
For a fair coin, yes. Previous outcomes do not affect future ones — this is the gambler's fallacy.