Force Calculator
Calculate force, mass, or acceleration using Newton's Second Law (F = ma). Includes worked examples, weight vs force explained, and net force calculations.
Newton's Second Law of Motion states that the force acting on an object equals its mass multiplied by its acceleration. Enter any two values to calculate the third.
Newton's Second Law Formula
F = m × a
Rearranged:
m = F ÷ a (mass from force and acceleration)
a = F ÷ m (acceleration from force and mass)
Where:
- F = Force in newtons (N)
- m = Mass in kilograms (kg)
- a = Acceleration in metres per second squared (m/s²)
What Is a Newton?
One newton (N) is the force required to accelerate a mass of 1 kilogram at 1 m/s². In everyday terms:
- The weight of a 100g apple ≈ 1 N
- Gravity on Earth accelerates objects at 9.81 m/s², so a 1kg object weighs 9.81 N
- A firm handshake grip exerts roughly 100–400 N
Worked Examples
Example 1 — Car braking
A 1,500 kg car decelerates at 8 m/s² (hard braking). What braking force is applied?
F = m × a = 1,500 × 8 = 12,000 N = 12 kN
At this deceleration, the car stops from 100 km/h (62 mph) in about 3.5 seconds.
Example 2 — Rocket launch
A rocket with a mass of 500,000 kg needs to accelerate upward at 15 m/s². What thrust force is needed?
First, gravity acts downward: F_gravity = 500,000 × 9.81 = 4,905,000 N
Net upward force needed: F_net = m × a = 500,000 × 15 = 7,500,000 N
Total thrust required = F_net + F_gravity = 7,500,000 + 4,905,000 = 12,405,000 N (12.4 MN)
Example 3 — Simple push
A 20 kg box is pushed with a force of 60 N. What is its acceleration?
a = F ÷ m = 60 ÷ 20 = 3 m/s²
Ignoring friction, the box accelerates at 3 m/s² — reaching 3 m/s (walking pace) in one second.
Weight vs Force: An Important Distinction
In physics, weight and mass are different things:
- Mass (kg) is the amount of matter in an object — it doesn't change wherever you are
- Weight (N) is the gravitational force acting on that mass — it changes with gravity
Weight (N) = mass (kg) × gravitational acceleration (m/s²)
W = m × g
On Earth: g = 9.81 m/s², so a 70 kg person weighs 70 × 9.81 = 686.7 N On the Moon: g = 1.62 m/s², same person weighs 70 × 1.62 = 113.4 N On Mars: g = 3.72 m/s², same person weighs 70 × 3.72 = 260.4 N
The person's mass is always 70 kg. Their weight depends on which planet they're standing on.
Net Force: When Multiple Forces Act
In real situations, multiple forces act on an object simultaneously. The net force is the vector sum of all forces:
F_net = F1 + F2 + F3 + ... (with direction signs)
Example — a box being pushed and sliding with friction:
- Applied push: +50 N (forward)
- Friction force: −20 N (backward)
- Net force: 50 − 20 = +30 N (forward)
- If box mass is 10 kg: a = 30 ÷ 10 = 3 m/s²
If net force is zero, the object is in equilibrium — it either stays still or moves at constant velocity (Newton's First Law).
Newton's Three Laws at a Glance
| Law | Statement | Formula |
|---|---|---|
| First | An object at rest stays at rest; an object in motion stays in motion unless a net force acts | F_net = 0 → constant velocity |
| Second | Force equals mass times acceleration | F = ma |
| Third | Every action has an equal and opposite reaction | F_AB = −F_BA |
Frequently Asked Questions
What is the difference between force and pressure?
Force (N) is the total push or pull. Pressure (Pa = N/m²) is force distributed over an area. A stiletto heel exerts the same force as a flat shoe but at much higher pressure because the contact area is tiny — this is why stilettos damage floors that flat shoes don't.
Can force be negative?
Force is a vector — it has direction. We choose a positive direction (usually up or to the right) and negative forces act in the opposite direction. A −50 N force just means 50 N in the opposite direction to our chosen positive. Net force being negative means the object accelerates in the negative direction.
Does Newton's Second Law work at all speeds?
For everyday speeds, yes. At speeds approaching the speed of light, relativistic effects mean that momentum (p = mv) doesn't change the same way — the correct relativistic form is F = dp/dt where p = γmv. At 99% of light speed, the relativistic mass factor γ ≈ 7, so a force produces much less acceleration than F = ma would predict.
What units can I use besides newtons and kilograms?
In the Imperial system, force is measured in pounds-force (lbf) and mass in slugs (not pounds — this is a common confusion). 1 pound-force = 4.448 newtons. 1 slug = 14.59 kg. If you use pounds for mass and feet/s² for acceleration, the unit of force is the poundal (pdl), not the pound-force.
How does Newton's Third Law relate to this?
For every force, there's an equal and opposite reaction force. When you push a box with 60 N, the box pushes back on you with 60 N. When a rocket engine produces 5 MN of thrust downward (gas expelled), the rocket experiences 5 MN upward (lift). The net force on the rocket is thrust minus weight, which determines its acceleration via F = ma.
What is the formula for gravitational force?
Newton's Law of Universal Gravitation: F = G × m1 × m2 ÷ r², where G = 6.674 × 10⁻¹¹ N·m²/kg², m1 and m2 are the two masses, and r is the distance between their centres. Near Earth's surface, this simplifies to F = mg where g = 9.81 m/s².
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