Geometric Series Sum and Nth Term Calculator
Calculates the nth term, finite sum, and infinite sum of a geometric series from the first term a and common ratio r. In...
Everyday arithmetic, algebra, and geometry — worked out clearly.
Percentages, fractions, ratios, geometry, and the little calculations that come up all the time — with formulas you can reuse anywhere.
Calculates the nth term, finite sum, and infinite sum of a geometric series from the first term a and common ratio r. In...
Approximates a definite integral using the composite Simpson's 1/3 rule from a table of function values at equally-space...
Calculates the sum of an infinite geometric series S = a/(1−r) for |r| < 1, and the finite partial sum S_n = a(1−r^n)/(1...
Computes y(t) = y₀ · e^(r·t) for continuous exponential growth (r > 0) or decay (r < 0). Also calculates the doubling ti...
Computes the first two convergents of a continued fraction from three partial quotients. Convergents are the best ration...
Approximates a definite integral using the composite trapezoidal rule from up to five equally-spaced function values.
Calculates the number of positive divisors of n = p₁^e₁ × p₂^e₂ × … as d(n) = (e₁+1)(e₂+1)…. For small n, also computes...
Calculates Euler's totient φ(n) = n × Π(1 − 1/p) for each distinct prime p dividing n. Used in RSA encryption and modula...
Calculates population P(t) using the logistic growth model with carrying capacity K, initial population P₀, and growth r...
Converts a complex number from rectangular form (a + bi) to polar form (r∠θ). Also computes the complex conjugate and mo...
Calculates a^e mod m using repeated squaring. Essential for RSA, Diffie-Hellman, and primality tests. Works for large va...
Calculates the cross product (scalar magnitude for 2-D vectors) and the angle between two 2-D vectors. The parallelogram...
Solves a system of two linear equations ax+by=e, cx+dy=f using Cramer's Rule. Computes the main determinant D and soluti...
For integers up to ~10^6, determines whether n is prime and outputs the prime factorisation as p₁^e₁ × p₂^e₂ … by trial...
Calculates the sum, product, and discriminant of the roots of a quadratic equation ax²+bx+c=0 using Vieta's formulas, wi...
Solves ax² + bx + c = 0 using the quadratic formula. Returns both roots, the discriminant Δ = b²−4ac (positive = 2 real,...
Calculates the Absolute Percentage Error (APE) between a forecast and actual value, plus the mean APE (MAPE) if multiple...
Calculates nPr = n!/(n−r)! (ordered arrangements) and nCr = n!/(r!(n−r)!) (unordered selections) for given n and r. Also...
Calculates the geometric mean of up to six positive values — the appropriate average for growth rates, ratios, and multi...
Finds the real cube root of the depressed cubic x³ + px + q = 0 using Cardano's formula: x = ∛(−q/2 + √D) + ∛(−q/2 − √D)...
Calculates the harmonic mean of up to six values — useful for averaging rates, speeds, and parallel circuit impedances.
Calculates the Standard Error of the Mean (SEM) from the sample standard deviation and sample size. Also gives the 95% c...
Solves for the missing side of a right triangle: hypotenuse c = √(a²+b²), or leg a = √(c²−b²). Also computes the triangl...
Calculates the nth Fibonacci number using Binet's closed-form formula and the sum of the first n Fibonacci numbers (S_n...