Force Calculator
Calculate force, mass, or acceleration using Newton's second law of motion (F = ma).
Newton's Second Law: F = ma
Quick Presets:
Force (F = ma)
98.1000 N
Calculation:
F = m × a = 10 kg × 9.81 m/s² = 98.1000 N
Weight Comparison:
Weight on Earth: 98.10 N (22.05 lbs)
Weight on Moon: 16.20 N
Weight on Mars: 37.10 N
Weight on Jupiter: 247.90 N
Newton's Second Law of Motion
Newton's second law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration. This fundamental law of physics can be written as F = ma, where F is force (in Newtons), m is mass (in kilograms), and a is acceleration (in meters per second squared).
Force Units
Newton (N)
SI unit of force. 1 N = 1 kg·m/s²
Pound-force (lbf)
Imperial unit. 1 lbf ≈ 4.448 N
Dyne (dyn)
CGS unit. 1 dyn = 10⁻⁵ N
Kilonewton (kN)
1 kN = 1000 N
What is Force?
Force is an interaction that causes an object to change its velocity (accelerate), change direction, or deform. Force is a vector quantity measured in Newtons (N).
| Property | Description | Unit |
|---|---|---|
| Magnitude | Strength of the force | Newtons (N) |
| Direction | Where the force points | Degrees or radians |
| Point of application | Where force acts on object | Position (m) |
| Line of action | Extended direction through point | — |
1 Newton is the force required to accelerate a 1 kg mass at 1 m/s².
Newton's Second Law
Where:
- F= Force (Newtons, N)
- m= Mass (kilograms, kg)
- a= Acceleration (m/s²)
Types of Forces
Forces are classified into contact and non-contact (field) forces:
| Force Type | Category | Example | Formula |
|---|---|---|---|
| Gravitational (Weight) | Non-contact | Objects falling | W = mg |
| Normal force | Contact | Book on table | N = mg (horizontal) |
| Friction | Contact | Sliding objects | f = μN |
| Tension | Contact | Rope pulling | T (varies) |
| Spring force | Contact | Compressed spring | F = -kx |
| Electromagnetic | Non-contact | Magnets, charges | F = kq₁q₂/r² |
| Applied force | Contact | Pushing a box | F_app (given) |
| Air resistance | Contact | Skydiving | F_drag = ½ρv²CdA |
Newton's Three Laws of Motion
Newton's laws form the foundation of classical mechanics:
| Law | Statement | Mathematical Form | Example |
|---|---|---|---|
| First Law (Inertia) | Objects stay at rest or in motion unless acted upon by a force | If ΣF = 0, then v = constant | Seat belts in cars |
| Second Law | Force equals mass times acceleration | ΣF = ma | Pushing a cart |
| Third Law | Every action has an equal and opposite reaction | F_AB = -F_BA | Rocket propulsion |
Net Force
Where:
- ΣF= Net (total) force
- ma= Mass times acceleration
Weight and Gravitational Force
Weight is the gravitational force acting on an object's mass:
| Location | g (m/s²) | Weight of 70 kg person |
|---|---|---|
| Earth (surface) | 9.81 | 687 N (154 lbs) |
| Moon | 1.62 | 113 N (25 lbs) |
| Mars | 3.71 | 260 N (58 lbs) |
| Jupiter | 24.79 | 1,735 N (390 lbs) |
| Space station (orbit) | ~0 | ~0 N (weightless) |
Note: Mass remains constant; weight changes with gravitational field strength.
Weight Formula
Where:
- W= Weight (N)
- m= Mass (kg)
- g= Gravitational acceleration (m/s²)
- G= Universal gravitational constant
Friction Forces
Friction opposes relative motion between surfaces:
| Type | Formula | When It Applies |
|---|---|---|
| Static friction | f_s ≤ μ_s N | Object at rest |
| Kinetic friction | f_k = μ_k N | Object sliding |
| Rolling friction | f_r = μ_r N | Wheels rolling |
| Surface Pair | μ_s (static) | μ_k (kinetic) |
|---|---|---|
| Rubber on concrete (dry) | 1.0 | 0.8 |
| Rubber on concrete (wet) | 0.7 | 0.5 |
| Steel on steel | 0.74 | 0.57 |
| Wood on wood | 0.5 | 0.3 |
| Ice on ice | 0.1 | 0.03 |
Friction Equations
Where:
- f= Friction force (N)
- μ= Coefficient of friction
- N= Normal force (N)
Free-Body Diagrams
A free-body diagram (FBD) shows all forces acting on an object:
| Step | Action | Note |
|---|---|---|
| 1 | Isolate the object | Draw as a point or simple shape |
| 2 | Identify all forces | Contact + non-contact forces |
| 3 | Draw force vectors | From center of object, to scale |
| 4 | Choose coordinate axes | Usually one axis along motion |
| 5 | Resolve into components | Use sin/cos for angled forces |
| 6 | Apply Newton's 2nd law | ΣFₓ = maₓ, ΣFᵧ = maᵧ |
Common forces to include: Weight (down), Normal (perpendicular to surface), Friction (opposing motion), Tension (along rope), Applied force.
Real-World Force Applications
Force calculations in everyday life:
| Application | Typical Force | Notes |
|---|---|---|
| Handshake | 5-50 N | Varies with grip |
| Pushing grocery cart | 20-50 N | To overcome friction |
| Bicycle braking | 200-400 N | Emergency stop |
| Car braking (4 wheels) | 5,000-15,000 N | Depends on speed, mass |
| Airplane thrust (jet) | 100,000-500,000 N | Per engine |
| Rocket launch (Saturn V) | 35,000,000 N | Total thrust |
Worked Examples
Calculate Force from Mass and Acceleration
Problem:
A 1,500 kg car accelerates at 3 m/s². What force does the engine provide?
Solution Steps:
- 1Identify given values: m = 1,500 kg, a = 3 m/s²
- 2Apply Newton's second law: F = ma
- 3Substitute: F = 1,500 × 3
- 4Calculate: F = 4,500 N
Result:
Engine force = 4,500 N (about 1,012 lbs)
Calculate Weight on Different Planets
Problem:
An astronaut has mass 75 kg. Calculate their weight on Earth and Mars.
Solution Steps:
- 1Earth: W = mg = 75 × 9.81 = 735.75 N
- 2Mars: W = mg = 75 × 3.71 = 278.25 N
- 3Ratio: Mars weight is 278/736 = 38% of Earth weight
Result:
Earth: 736 N, Mars: 278 N
Friction Force Problem
Problem:
A 20 kg box on a floor (μ_k = 0.3) is pushed horizontally. What force is needed for constant velocity?
Solution Steps:
- 1At constant velocity, applied force = friction
- 2Normal force: N = mg = 20 × 9.81 = 196 N
- 3Friction: f = μN = 0.3 × 196 = 58.9 N
- 4Required push force = 58.9 N
Result:
Applied force needed = 58.9 N
Tips & Best Practices
- ✓Always draw a free-body diagram before solving force problems
- ✓Weight always points straight down toward Earth's center
- ✓Normal force is perpendicular to the contact surface, not always vertical
- ✓Friction opposes relative motion (or potential motion), not the applied force
- ✓When ΣF = 0, velocity is constant (including zero)—not necessarily at rest
- ✓Convert weight in pounds to Newtons: multiply by 4.45
- ✓Action-reaction pairs act on different objects—they never cancel
Frequently Asked Questions
Sources & References
Last updated: 2026-01-22