Mechanics Calculators

Mechanics is the physics of forces and motion: what makes an object speed up, slow down, rotate, or stay exactly where it is. Nearly all of it follows from Newton's three laws, with F = ma as the working equation — once you know the net force on a mass you know its acceleration, and from acceleration you get velocity and position over time.

Mechanics calculators

Newton's Second Law

Calculate force from mass and acceleration with Newton's second law, F = ma.

F = m × a

Acceleration

Calculate acceleration from initial velocity, final velocity and time.

a = (v₁ − v₀) / t

Momentum

Calculate momentum from mass and velocity (p = mv).

p = m × v

Projectile Motion

Calculate the range, maximum height and flight time of a projectile from launch speed and angle.

R = v₀² · sin(2θ) / g

Free Fall

Calculate free fall distance, time and impact speed from height.

t = √(2h/g), v = √(2gh)

Torque

Calculate torque from force, lever arm length and angle.

τ = r × F × sin(θ)

Terminal Velocity

Calculate terminal velocity from mass, drag coefficient, cross-sectional area and air density.

v = √(2mg / (ρ·A·Cd))

Tension

Calculate the tension in a rope, cable or string holding or lifting a mass, with or without acceleration.

T = m × (g + a)

Atwood Machine

Calculate the acceleration and rope tension of an Atwood machine — two masses over a frictionless pulley.

a = (m₁ − m₂)g / (m₁ + m₂), T = 2·m₁·m₂·g / (m₁ + m₂)

Incline Tension

Calculate the rope tension needed to pull a block up a rough incline at steady speed.

T = m·g·(sin θ + μ·cos θ)

Two-Rope Tension

Calculate the tension in each of two symmetric ropes or cables holding a hanging weight — a sign, lamp or load suspended from two anchors at an angle.

T = m·g / (2·sin θ)

Impact Force

Calculate the average impact force of a collision from mass, impact speed and stopping distance.

F = m·v² / (2·d)

Horizontal Projectile

Calculate the range, fall time and impact speed of a projectile launched horizontally from a height.

R = v·√(2h/g)

Hooke's Law

Calculate spring force from stiffness and stretch using Hooke's law (F = kx), plus the elastic potential energy stored.

F = k × x

When to reach for these

Reach for these when you need a number rather than an intuition: the force needed to stop a given mass in a given distance, how far a ball thrown at 15 m/s travels before it lands, the torque a spanner delivers at the end of its handle, or the tension carried by each of two ropes holding a sign. Unless a calculator states otherwise it assumes rigid bodies, gravity of 9.81 m/s², and no air resistance — the terminal-velocity calculator is the one that models drag explicitly.

Mechanics Calculators