Normal Distribution Calculator
Normal distribution calculator
Compute lower-tail, upper-tail, or interval probability for a normal distribution.
Result
0.8041735512
Interval probability P(-1.2 ≤ X ≤ 1.4).
stats
Advanced options
Flow
- Enter mean and standard deviation.
- Choose lower-tail, upper-tail, or interval mode.
- Provide x or bounds and read resulting probability.
Example
Worked example: μ=0, σ=1, interval [-1.2, 1.4]
- 1 Compute z-values for both bounds.
- 2 Evaluate CDF at upper and lower bounds.
- 3 Probability = Φ(1.4) - Φ(-1.2) ≈ 0.8046
Interval probability is approximately 0.8046.
How
- Enter mean and standard deviation.
- Choose lower-tail, upper-tail, or interval mode.
- Provide x or bounds and read resulting probability.
Avoid
- Using variance value directly instead of standard deviation.
- Mixing up lower-tail and upper-tail interpretations.
- Applying normal model to strongly skewed data without diagnostics.
Checks
Best fit
Normal Distribution Calculator is built for compute normal-distribution lower-tail, upper-tail, and interval probabilities. If Normal Distribution Calculator does not match the input scope, compare the answer with a second method.
Input check
Match the entered values to this rule before copying the answer: P(X≤x)=Φ((x-μ)/σ), P(a≤X≤b)=Φ((b-μ)/σ)-Φ((a-μ)/σ).
Sanity check
For Normal Distribution Calculator, use the worked example as a quick benchmark: Interval probability is approximately 0.8046. If the normal distribution calculator answer is far away, check whether an input, unit, or mode changed.
Before copying
Review this common issue first: using variance value directly instead of standard deviation.
FAQ
Can I use non-standard normal parameters?
Yes. Enter any mean and positive standard deviation.
What if standard deviation is zero?
The distribution becomes degenerate, so this tool requires positive standard deviation.
Is this exact or approximate?
CDF uses high-accuracy numerical approximation suitable for practical analysis.
Switch
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