Developer Utilities
Small developer utilities that save a trip to a random website. Encode and decode Base64, explain a regex, build UTM links, generate QR codes and vCards, and more — the everyday helpers. Free in your browser, and available by API when you need them in a script.
Developer Utilities
Critical angle total internal reflection calculator
POST /trig/critical-angle$0.002Developer Utilities
Solar declination approximation calculator
cosine axial tilt model
POST /trig/declination-approx$0.002Developer Utilities
Parallelogram diagonal calculator from sides and angle
POST /trig/diagonal-of-parallelogram$0.002Developer Utilities
Distance to horizon calculator
range from observer height, free
POST /trig/horizon-distance$0.002Developer Utilities
Isosceles triangle from leg and apex angle calculator
POST /trig/isosceles-triangle-from-apex$0.002Developer Utilities
Tidal height sinusoid model
water level from high, low, and period
POST /trig/model-tide-sinusoid$0.002Developer Utilities
Regular polygon apothem calculator from circumradius
POST /trig/regular-polygon-apothem$0.002Developer Utilities
Tangent from line slope calculator
inclination angle in degrees
POST /trig/tangent-from-slope$0.002Developer Utilities
Triangle height from base and two base angles calculator
POST /trig/triangle-height-two-angles$0.002Developer Utilities
Triangle angle from side and altitude calculator
asin(h/s)
POST /trig/triangle-angle-from-side-altitude$0.002Developer Utilities
Derivative of Logarithmic Function Calculator
POST /calculus/derivative-logarithm$0.002Developer Utilities
Power Rule Derivative Calculator for a·x^n
POST /calculus/derivative-power-rule$0.002Developer Utilities
Infinite limit from the right calculator for rational functions
POST /calculus/limit-infinite-from-right$0.002Developer Utilities
Limit Product and Quotient Rule Calculator
POST /calculus/limit-product-quotient$0.002Developer Utilities
Equation of tangent line calculator
find slope and intercept
POST /calculus/tangent-line-equation$0.002Developer Utilities
Implicit Derivative of an Ellipse Calculator
POST /calculus/implicit-derivative-ellipse$0.002Developer Utilities
Concave up intervals calculator
where p″(x) > 0 for a polynomial
POST /calculus/concave-up-intervals$0.002Developer Utilities
Critical Points of a Polynomial Calculator
POST /calculus/critical-points-polynomial$0.002Developer Utilities
Derivative sign at a point calculator
increasing or decreasing
POST /calculus/derivative-sign-at-point$0.002Developer Utilities
Increasing or Decreasing at a Point Calculator
POST /calculus/increasing-decreasing-test$0.002Developer Utilities
Inflection points of a polynomial calculator
POST /calculus/inflection-points-polynomial$0.002Developer Utilities
Minimum Sum with a Fixed Product Optimization Calculator
POST /calculus/optimization-min-sum-fixed-product$0.002Developer Utilities
Rolle's Theorem Point Finder Calculator
POST /calculus/rolle-theorem-point$0.002Developer Utilities
Secant line slope calculator for two points
POST /calculus/secant-line-slope$0.002Developer Utilities
Horizontal tangent points calculator
solve f′(x)=0 for a polynomial
POST /calculus/tangent-horizontal-points$0.002Developer Utilities
Two-Point Gauss-Legendre Quadrature Calculator
POST /calculus/gauss-legendre-2point$0.002Developer Utilities
Improper integral of exponential calculator
∫₀^∞ a e^{-kx} dx
POST /calculus/improper-integral-exponential$0.002Developer Utilities
Indefinite Integral of Polynomial Calculator
POST /calculus/indefinite-integral-polynomial$0.002Developer Utilities
Polynomial even/odd symmetry checker
classify by exponent parity
POST /calculus/polynomial-symmetry$0.002Developer Utilities
Simpson's three-eighths rule calculator for definite integrals
POST /calculus/simpson-three-eighths$0.002Developer Utilities
Accumulation Function Value Calculator
POST /calculus/accumulation-function$0.002Developer Utilities
Center of Mass from Density Calculator
POST /calculus/center-of-mass-1d$0.002Developer Utilities
Centroid X-Coordinate of a Region Calculator
POST /calculus/centroid-region-x$0.002Developer Utilities
Finite geometric series partial sum
S_n = a(1−r^n)/(1−r)
POST /calculus/geometric-series-sum-finite$0.002Developer Utilities
Moment of a Region About the X-Axis Calculator
POST /calculus/moment-region-x$0.002Developer Utilities
Net Signed Area Calculator for Polynomials
POST /calculus/net-signed-area$0.002Developer Utilities
Radius of convergence from coefficients calculator
POST /calculus/power-series-radius$0.002Developer Utilities
Midpoint Riemann sum calculator
approximate ∫ₐᵇ f(x) dx
POST /calculus/riemann-sum-midpoint$0.002Developer Utilities
Taylor Coefficients of Natural Log Calculator
POST /calculus/taylor-coefficients-ln$0.002Developer Utilities
Euler Method ODE Solver Calculator
Step-by-Step Table
POST /calculus/euler-method-step$0.002Developer Utilities
P-series convergence checker
test whether a series converges
POST /calculus/p-series-convergence$0.002Developer Utilities
Series Partial Sum Calculator
Add the First n Terms
POST /calculus/partial-sum-series$0.002Developer Utilities
Sum of the first n cubes calculator
1³+…+n³ = (n(n+1)/2)²
POST /calculus/sum-of-cubes-formula$0.002Developer Utilities
Damped oscillator position calculator
x(t)=A e^{-βt} cos(ωt+φ)
POST /calculus/damped-oscillator-position$0.002Developer Utilities
ODE half-life from decay constant calculator
ln(2) / lambda
POST /calculus/half-life-from-decay-constant$0.002Developer Utilities
Runge-Kutta 4 single-step calculator
compute RK4 slopes
POST /calculus/rk4-single-step$0.002Developer Utilities
Separable Differential Equation Solver Calculator
POST /calculus/separable-ode$0.002Developer Utilities
Series sum by partial fractions
telescoping closed form calculator
POST /calculus/series-sum-by-partial-fractions$0.002Developer Utilities
Euler Method for a 2D System Calculator
Show Every Step
POST /calculus/euler-method-system-2d$0.002Developer Utilities
Fixed-point iteration single-step calculator
apply g once to x_n
POST /calculus/fixed-point-single-step$0.002Developer Utilities
Mixing tank concentration calculator
first-order ODE C(t), free
POST /calculus/mixing-tank-concentration$0.002Developer Utilities
Taylor Series Method ODE Calculator
POST /calculus/taylor-method-ode$0.002Developer Utilities
Natural cubic spline interpolation calculator
evaluate S(x) at a target
POST /calculus/cubic-spline-natural$0.002Developer Utilities
Inverse interpolation calculator
estimate x from target y, free
POST /calculus/inverse-interpolation$0.002Developer Utilities
Least squares residuals calculator
residuals and residual sum of squares
POST /calculus/least-squares-residuals$0.002Developer Utilities
Least-squares regression prediction calculator
POST /calculus/linear-regression-predict$0.002Developer Utilities
Newton Backward Difference Interpolation Calculator
POST /calculus/newton-backward-interpolation$0.002Developer Utilities
Newton-Raphson Single Step Calculator
POST /calculus/newton-raphson-single-step$0.002Developer Utilities
Steffensen method root finder calculator
quadratic convergence
POST /calculus/steffensen-method$0.002Developer Utilities
Double Integral Midpoint Rule Calculator
POST /calculus/double-integral-midpoint$0.002