Solve any equation forward or backward—click any variable to make it the target with automatic SI unit conversions.
Solve z = (x - μ) / σ for standard normal Z-score, raw observation x, population mean μ, or standard deviation σ.
Solve SE = s / √n for standard error of the sample mean, sample standard deviation s, or required sample size n.
Solve MOE = z × (σ / √n) for confidence interval half-width, critical Z-score, population standard deviation, or sample size n.
Solve Cochran's sample size formula n = z² × p(1 - p) / E² for required respondents n, margin of error E (%), critical z*, or baseline proportion p.
Solve CV (%) = (σ / μ) × 100 for relative standard deviation (CV), standard deviation σ, or sample mean μ.
Solve b₁ = r × (s_y / s_x) for ordinary least-squares regression slope b₁, Pearson correlation r, response standard deviation s_y, or predictor standard deviation s_x.
Solve OR = (p₁ / (1 - p₁)) / (p₂ / (1 - p₂)) for epidemiological Odds Ratio, treatment event probability p₁, or control event probability p₂.
Solve P(A|B) = (P(B|A) × P(A)) / P(B) for posterior probability, prior probability P(A), likelihood sensitivity P(B|A), or marginal evidence P(B).
Solve μ = λ × t for expected Poisson arrival count μ, arrival rate λ per unit time, or observation window t.
Solve μ = n × p for expected binomial successes μ, number of independent Bernoulli trials n, or single-trial success probability p.
Solve E[X] = k / p for the expected number of trials to achieve k successes (set k = 1 for the Geometric distribution), target successes k, or trial probability p.
Solve S = (R_p - R_f) / σ_p for annualized Sharpe Ratio, portfolio return R_p, risk-free rate R_f, or annualized portfolio volatility σ_p.
Solve t = (x̄ - μ₀) / (s / √n) for Student's t-statistic, sample mean x̄, null hypothesis mean μ₀, sample standard deviation s, or sample size n.
Solve d = (M₁ - M₂) / SD_pooled for Cohen's d standardized effect size, treatment mean M₁, control mean M₂, or pooled standard deviation.