Force Calculator
Calculate force, weight, friction, gravitational attraction and pressure with step-by-step workings
// Newton's Laws of Motion
Newton's Laws and Force
Force is a push or pull that causes an object to accelerate, decelerate or change direction. It is measured in Newtons (N), where 1 N is the force needed to accelerate 1 kg at 1 m/s².
Formulas
Weight vs Mass
Mass is the amount of matter in an object (kg) — it is constant everywhere. Weight is the gravitational force acting on that mass (N) — it varies with location. A 70 kg person weighs 686 N on Earth but only 113 N on the Moon.
Force and F = ma: The Equation That Runs Everything
Built and verified by Andrius R. · Updated June 2026
Newton's second law is three symbols that explain car crashes, rocket launches, why bathroom scales lie on the Moon, and what a "newton" of force actually feels like. Here's the equation with its units made tangible.
What a newton is, in hand terms
1 N = the force that accelerates 1 kg by 1 m/s². For intuition: a newton is roughly the weight of a small apple (~102 g) resting in your palm — Newton, apple, the units gods were kind. A 70 kg person's weight is 70 × 9.81 = ~687 N; a firm handshake is tens of newtons; a car engine's push at the wheels, thousands.
Worked example: the force inside an ordinary acceleration
Acceleration: (100 ÷ 3.6) ÷ 8 ≈ 3.5 m/s². For a 1,500 kg car: F = 1,500 × 3.5 ≈ 5,200 N of net forward force. Run it backwards for a crash: stopping from 50 km/h (13.9 m/s) in 0.1 s — hitting a wall — demands a deceleration of 139 m/s², so a 75 kg occupant experiences ~10,400 N, the weight of more than a tonne. Crumple zones, airbags and seatbelts all work by one trick: stretching the stopping time, which divides the force. Same physics as bending your knees when you land a jump.
Mass vs weight: the distinction with real consequences
Mass (kg) is how much matter you are; weight (N) is the gravitational force on that matter: W = m × g. On Earth g ≈ 9.81 m/s²; on the Moon 1.62; on Mars 3.71. Your 70 kg mass is 70 kg everywhere, but it weighs 687 N here, 113 N on the Moon. Bathroom scales measure force and quietly divide by Earth's g to display "kilograms" — honest at home, a lie anywhere else. The everyday habit of quoting weight in kg works because we all share one planet; engineering and rocketry can't afford the shortcut, and mixing the two (kilogram-force vs newtons) has contributed to real disasters — see the conversion-failure stories in the unit converter guide.
The three laws in one paragraph each
- Inertia: no net force, no change in motion. Seatbelts exist because in a crash the car stops but, per the first law, you don't.
- F = ma: the quantitative core — force causes acceleration in proportion to mass. Same push, double the mass, half the acceleration; why empty shopping carts and loaded ones feel like different machines.
- Action–reaction: forces come in equal-opposite pairs. You push the ground backwards to walk; a rocket pushes exhaust down and the exhaust pushes the rocket up — no air to "push against" required, which is why rockets work in vacuum.
Net force: the word that prevents most confusion
F = ma uses the net force — the sum of all pushes and pulls. A car cruising at a steady 120 km/h has a large engine force exactly canceled by drag and friction: net zero, acceleration zero, first law satisfied. An object can be drowning in forces and still not accelerate. When a force problem gives a weird answer, the missing force (friction, drag, the normal force from the ground) is almost always the culprit — and it's why "constant speed" in any physics problem is code for "the forces balance."
From the Blog
// Weight ≠ Mass
Mass is measured in kg; weight is a force in Newtons. 70 kg on Earth weighs 686 N. The same mass on the Moon weighs only 113 N.
// Friction Basics
Static friction (preventing motion) is slightly higher than kinetic friction (resisting ongoing motion). This is why it's harder to start sliding than to keep sliding.
// Pressure Example
A stiletto heel (1 cm² area) at 60 kg exerts: P = 588 N / 0.0001 m² = 5.88 MPa — greater than a car tyre pressure by 100×.
// g Varies
g is not exactly 9.81 everywhere. It's ~9.78 at the equator (centrifugal effect) and ~9.83 at the poles. Altitude also reduces g slightly.