Force Calculator
Calculate force, mass, or acceleration using Newton's Second Law (F=ma). Find gravitational force, friction, and net force with unit conversions.
Force
98.1000 N
Force
98.1000 N
Mass
10.0000 kg
Acceleration
9.8100 m/s²
Calculation Details
Newton's Second Law: F = m × a
98.10 N = 10.00 kg × 9.81 m/s²
Weight (at Earth's surface): 98.07 N
Unit Conversions
Force: 98.10 N = 0.0981 kN
Force: 98.10 N = 22.05 lbf
Mass: 10.00 kg = 22.05 lb
Accel: 9.81 m/s² = 1.000 g
Common Reference Values
- • Earth gravity: g = 9.81 m/s² (1 g)
- • 1 Newton ≈ force of a small apple
- • Human walking: ~2-3 m/s²
- • Car braking: ~3-8 m/s²
- • Fighter jet: up to 9 g
About This Calculator
Force is the push or pull that causes an object to accelerate. Newton's Second Law, F = ma, describes the relationship between force, mass, and acceleration. This fundamental equation is the cornerstone of classical mechanics and essential for physics, engineering, and everyday problem-solving.
What is Force? Force is any interaction that changes an object's motion. When you push a shopping cart, gravity pulls you down, or friction slows your car, these are all forces. The SI unit of force is the Newton (N), where 1 N = 1 kg·m/s².
Newton's Second Law: F = m × a
- F = Force (Newtons)
- m = Mass (kilograms)
- a = Acceleration (m/s²)
Why Force Matters:
- Designing structures and machines
- Understanding vehicle dynamics
- Calculating rocket thrust
- Analyzing sports performance
- Engineering safety systems
This calculator handles force, mass, and acceleration calculations with unit conversions. For motion analysis, see our Velocity Calculator and Acceleration Calculator.
How to Use the Force Calculator
- 1Select what you want to calculate: force, mass, or acceleration.
- 2Enter the two known values.
- 3Select appropriate units for each value.
- 4The calculator computes the unknown value.
- 5Review the result in SI units (N, kg, m/s²).
- 6Check unit conversions for other systems.
- 7Compare with reference values for context.
- 8Use weight calculation for gravitational force.
- 9Verify your answer makes physical sense.
- 10Apply to real-world problems.
Newton's Second Law
The fundamental relationship between force, mass, and acceleration.
The Three Forms
F = m × a (find force) m = F / a (find mass) a = F / m (find acceleration)
What Each Means
Force (F): The push or pull causing acceleration
- Measured in Newtons (N)
- 1 N = 1 kg·m/s²
Mass (m): Amount of matter
- Measured in kilograms (kg)
- Resistance to acceleration (inertia)
Acceleration (a): Rate of velocity change
- Measured in m/s²
- Includes speeding up, slowing down, turning
Example Calculation
A 1000 kg car accelerates at 3 m/s²: F = 1000 kg × 3 m/s² = 3000 N (3 kN)
This is the net force required to accelerate the car.
Types of Forces
Different forces we encounter in physics.
Contact Forces
Normal Force (N): Perpendicular to surface contact Friction (f): Opposes relative motion between surfaces Tension (T): Pull through rope, string, or cable Applied Force: Direct push or pull
Non-Contact Forces
Gravity (Fg): Attractive force between masses Fg = G × (m₁ × m₂) / r²
On Earth's surface: Fg = m × g where g = 9.81 m/s²
Electromagnetic: Between charged particles Nuclear: Within atomic nuclei
Friction Details
Static friction: fs ≤ μs × N Kinetic friction: fk = μk × N
Where:
- μs = coefficient of static friction
- μk = coefficient of kinetic friction
- N = normal force
Common Friction Coefficients
| Surface | μs | μk |
|---|---|---|
| Rubber on concrete | 1.0 | 0.8 |
| Wood on wood | 0.5 | 0.3 |
| Steel on steel | 0.6 | 0.4 |
| Ice on ice | 0.1 | 0.03 |
Weight vs. Mass
Understanding the crucial difference.
Mass (m)
- Amount of matter in an object
- Intrinsic property (doesn't change with location)
- Measured in kilograms (kg)
- Scalar quantity
Weight (W)
- Force of gravity on an object
- Depends on location (gravitational field)
- Measured in Newtons (N)
- Vector quantity (has direction: downward)
The Relationship
W = m × g
Where g = gravitational acceleration
| Location | g (m/s²) | 70 kg person weight |
|---|---|---|
| Earth | 9.81 | 687 N |
| Moon | 1.62 | 113 N |
| Mars | 3.72 | 260 N |
| Jupiter | 24.79 | 1,735 N |
Common Confusion
"I weigh 70 kilograms" is technically incorrect.
- Your mass is 70 kg
- Your weight (on Earth) is 686.7 N
- Colloquially, "weight in kg" means mass
Weightlessness
In orbit, you're in freefall - you don't feel weight, but your mass is unchanged and gravity still acts on you.
Net Force and Free Body Diagrams
Analyzing multiple forces on an object.
Net Force
ΣF = F_net = m × a
The vector sum of all forces determines acceleration.
Free Body Diagrams
Steps to draw:
- Identify the object
- Draw it as a point or simple shape
- Draw all forces as arrows from the center
- Label each force
- Include coordinate axes
Example: Block on Incline
Forces on a block sliding down a 30° incline:
- Weight (W = mg): straight down
- Normal (N): perpendicular to surface
- Friction (f): parallel to surface, opposing motion
Equilibrium
When ΣF = 0, the object is in equilibrium:
- Static equilibrium: at rest
- Dynamic equilibrium: constant velocity
Breaking Into Components
For incline problems:
- Parallel: F∥ = mg sin(θ)
- Perpendicular: F⊥ = mg cos(θ)
Normal force: N = mg cos(θ) Acceleration: a = g sin(θ) - μk g cos(θ)
Common Applications
Real-world force calculations.
Vehicle Dynamics
Stopping distance: Requires force analysis
- Braking force = μ × m × g
- Stopping distance = v² / (2 × μ × g)
Acceleration: Engine force minus resistance F_net = F_engine - F_drag - F_rolling
Structural Engineering
Load calculations:
- Dead loads (permanent)
- Live loads (temporary)
- Dynamic loads (impact)
Safety factor: Designed strength / Expected load
Sports Science
Sprint start: F = m × a Elite sprinters: 3-4× body weight horizontal force
Jumping: F_avg × t = m × Δv Vertical jump requires overcoming weight + generating velocity
Aerospace
Rocket thrust: F = ṁ × v_exhaust Must exceed weight for liftoff
Orbital mechanics: F = G × M × m / r²
Common Force Values
| Situation | Force |
|---|---|
| Picking up phone | ~1 N |
| Handshake | 20-50 N |
| Pushing shopping cart | 30-50 N |
| Car engine force | 3,000-10,000 N |
| Rocket launch | 10,000,000+ N |
Units and Conversions
Force units across different systems.
SI Unit: Newton (N)
1 N = 1 kg × 1 m/s² = 1 kg·m/s²
The force required to accelerate 1 kg at 1 m/s².
Other Units
| Unit | Symbol | Conversion |
|---|---|---|
| Newton | N | 1 N |
| Kilonewton | kN | 1000 N |
| Meganewton | MN | 1,000,000 N |
| Pound-force | lbf | 4.448 N |
| Kilogram-force | kgf | 9.807 N |
| Dyne | dyn | 0.00001 N |
Mass Units
| Unit | Conversion to kg |
|---|---|
| Kilogram | 1 kg |
| Gram | 0.001 kg |
| Pound (mass) | 0.4536 kg |
| Slug | 14.59 kg |
Acceleration Units
| Unit | Conversion to m/s² |
|---|---|
| m/s² | 1 |
| ft/s² | 0.3048 |
| g (standard gravity) | 9.80665 |
Quick Conversions
- 1 lbf ≈ 4.45 N
- 1 kgf ≈ 9.81 N (weight of 1 kg on Earth)
- 1 ton-force ≈ 9,807 N
Pro Tips
- 💡Always identify all forces before solving: gravity, normal, friction, applied, etc.
- 💡Draw a free body diagram to visualize forces.
- 💡Net force, not individual forces, determines acceleration.
- 💡Mass is constant; weight depends on location.
- 💡Check units: F (N) = m (kg) × a (m/s²).
- 💡1 Newton ≈ weight of a small apple (100g on Earth).
- 💡Friction always opposes motion (or potential motion).
- 💡Normal force is perpendicular to the contact surface.
- 💡On inclines, break forces into parallel and perpendicular components.
- 💡Zero net force means zero acceleration, not zero motion.
- 💡Weight = mg where g = 9.81 m/s² on Earth.
- 💡For rockets, use full momentum equation when mass changes.
Frequently Asked Questions
Mass is the amount of matter in an object (measured in kg), while weight is the gravitational force on that mass (measured in N). Mass is constant everywhere; weight depends on gravitational field strength. On Earth, Weight = mass × 9.81 m/s².
