Kinematics
Kinematics
Calculators & Tools
Arrow Speed Calculator
The Arrow Speed Calculator estimates real-world arrow velocity in feet per second (fps) by adjusting a bow's manufacturer IBO rating for your actual draw length, draw weight, arrow weight, and string accessories. It also calculates kinetic energy in ft·lbf and momentum in slug·fps, and classifies the result by hunting game class from small game through the toughest big game.
Quarter Mile Calculator
Estimates quarter mile elapsed time (ET) and trap speed from vehicle horsepower and weight using Hale's formula, and solves the inverse problems of deriving HP from a known ET or trap speed. Includes 1/8 mile estimate, 0-60 mph estimate, and NHRA class classification.
Free Fall Calculator
The Free Fall Calculator solves for any free fall variable (time, impact velocity, height fallen, or initial velocity) using standard kinematic equations under constant gravitational acceleration. It includes a planet/gravity body selector covering Earth, Moon, Mars, Jupiter, Venus, and Mercury, displays results in m/s, km/h, and mph, and shows a full step-by-step calculation breakdown alongside a reference table of impact speeds from common heights.
Ballistic Coefficient Calculator
The Ballistic Coefficient Calculator computes a bullet's ballistic coefficient (BC) from its mass in grains, diameter in inches, and form factor. It supports both G1 and G7 drag models, shows the full calculation breakdown including sectional density and cross-sectional area, provides form factor presets for common bullet shapes, and classifies the resulting BC from low through excellent with practical effective-range guidance.
Rolling Resistance Calculator
Calculates rolling resistance force (Fr = Crr × m × g), power consumed (P = Fr × v), grade resistance force, and total resistance from vehicle mass, rolling resistance coefficient, speed, and road gradient. Supports kg/lbs and m/s/km/h/mph unit toggles.
Free Fall with Air Resistance Calculator
The Free Fall with Air Resistance Calculator uses Euler numerical integration to simulate the velocity of a falling object over time under combined gravitational and aerodynamic drag forces. It computes terminal velocity using v_t = sqrt(2mg / rho*Cd*A), simulates the full velocity profile from rest to impact, and compares actual impact speed against ideal free fall (no drag). Inputs: mass, drag coefficient, cross-sectional area, fall height, and air density. Presets cover skydivers (belly and head-down), baseball, golf ball, feather, and bowling ball.
Car Jump Distance Calculator
The Car Jump Distance Calculator uses projectile motion physics to calculate how far a car travels through the air after launching off a ramp. Enter launch speed in mph, ramp angle in degrees, and ramp height above the landing zone in feet to get horizontal jump distance in both feet and meters, total air time, peak height, landing speed, and landing angle. Results appear instantly and update live as you type. Includes preset stunt scenarios and a famous car jump reference table.
Trajectory Calculator
Calculates and visualises the full parabolic trajectory of a projectile from launch speed, angle, and height. Returns range, max height, time of flight, impact speed, impact angle, and a 12-point trajectory table. Renders an SVG arc diagram with the peak highlighted.
Horizontal Projectile Motion Calculator
The Horizontal Projectile Motion Calculator computes the complete trajectory of an object launched horizontally from a height with zero initial vertical velocity. Enter the launch height and horizontal speed to instantly get time of flight, horizontal range, impact speed, impact angle, and a six-step trajectory table showing position and velocity throughout the flight. Supports metric and imperial units with six real-world scenario presets.
Displacement Calculator
The Displacement Calculator solves for displacement using all four standard kinematics formulas. Select which variables you know (velocity and time, initial velocity plus acceleration and time, initial and final velocity plus time, or initial and final velocity plus acceleration) and the calculator returns the displacement in metres with a step-by-step breakdown showing how each formula was applied.
Friction Calculator
The Friction Calculator computes normal force, maximum static friction force, kinetic friction force, net force, and resulting acceleration for objects on flat surfaces (with applied force) or inclined planes. It determines whether the object will slide based on comparing applied force or gravity component against the maximum static friction threshold. Includes presets for common material pairs (rubber on concrete, steel on steel, wood on wood, ice, Teflon) and a reference table of friction coefficients.
Ground Speed Calculator
The Ground Speed Calculator computes aircraft ground speed from true airspeed and wind using vector addition. It shows track over ground, wind correction angle (crab angle), headwind component, tailwind component, crosswind component, and estimated flight time from an optional distance input. Includes six scenario presets and a unit toggle for knots, mph, and km/h.
Conservation of Momentum Calculator
The Conservation of Momentum Calculator solves 1D two-body collisions for three collision types: elastic (both momentum and kinetic energy conserved), partially inelastic (momentum conserved, some KE lost), and perfectly inelastic (objects stick together). Enter the mass and initial velocity of each object to get the final velocities, total momentum, kinetic energy before and after, and the percentage of kinetic energy lost in the collision.
Resultant Velocity Calculator
Adds two or more velocity vectors in 2D or 3D by summing their Cartesian components, then returns the resultant magnitude, direction angle from the positive x-axis, elevation angle (3D), and individual vector magnitudes. Supports up to unlimited vectors with a dynamic add/remove interface.
Projectile Motion Calculator
A projectile follows a parabolic path because horizontal velocity stays constant while vertical velocity changes at 9.81 m/s² downward. Range, maximum height, and flight time all follow directly from those two independent motions. This calculator handles forward solve, reverse angle-finding (returning both the low-arc and high-arc solutions), reverse speed-finding, real air-drag computation via RK4 numerical integration, and eight named real-world scenarios from basketball free throws to historical cannon shots.
Side Slip Calculator
Determines whether a vehicle will side slip in a turn by comparing required centripetal acceleration (v²/r) against maximum available lateral acceleration from friction and banking ((μ + tan θ)/(1 - μ tan θ) × g). Returns slip status, safety margin, max safe speed, and minimum safe radius.
Time of Flight Calculator
Calculates total time of flight for a projectile launched at a given speed, angle, and height above landing level using the quadratic formula derived from vertical SUVAT equations. Returns total flight time, time to peak, horizontal range, and maximum height. Supports metric and imperial speed units.
Velocity Calculator
Solves for any one of the five SUVAT kinematic variables (v, u, a, t, s) given at least three others. Supports m/s, km/h, mph for speed; m, km, ft, mi for displacement. Results update in real time with 300ms debounce. Solved variable is highlighted in the results panel.
Terminal Velocity Calculator
Calculates terminal velocity using vt = sqrt(2mg / (rho * Cd * A)), where m is mass, g is gravitational acceleration, rho is air density, Cd is drag coefficient, and A is cross-sectional area. Returns terminal velocity in m/s, km/h, and mph, plus the equilibrium drag force.
Projectile Range Calculator
Calculates horizontal range of a projectile from launch speed and angle, and also solves the inverse problems: required speed for a target range, or launch angle for a given speed and range. Displays complementary angle pairs and a range-vs-angle comparison table.