Force Calculator F=ma • Weight • Friction • Centripetal • Impulse • Gravitation — Step-by-Step
The most complete free force calculator — six physics modes in one tool. F=ma mode: solve for force, mass, or acceleration bidirectionally — leave any one field blank and the calculator solves for it. Full unit support: kg, g, lb, slug for mass; N, kN, lbf, kgf, dyn for force; m/s², ft/s², g for acceleration. Weight mode: W=mg with 7 planetary gravity values (Earth, Moon, Mars, Jupiter, Venus, Saturn, Sun). Friction mode: f=μN solving for any of friction force, coefficient of friction, or normal force. Centripetal: Fc=mv²/r. Impulse: J=FΔt or J=mΔv. Universal gravitation: F=Gm₁m₂/r². Every result includes step-by-step working, unit conversions, real-world force context, and a free body diagram. All browser-side — no account required.
Six physics modes — F=ma, Weight, Friction, Centripetal, Impulse, Gravitation
Force quick reference
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Newton’s Three Laws of Motion — The Foundation of Force Calculations
F=ma Calculator — How to Calculate Force, Mass & Acceleration
Newton’s Second Law states that the net force acting on an object equals the product of its mass and acceleration: F = m × a. This single equation is the foundation of classical mechanics. It can be rearranged to solve for any of the three variables.
The force formula — three variants
Acceleration: a = F / m (m/s² = N / kg)
Mass: m = F / a (kg = N / (m/s²))
How to calculate force step by step
Step 1: Write the formula: F = m × a
Step 2: F = 1200 kg × 3 m/s²
Step 3: F = 3600 N = 3.6 kN
Example: How to calculate acceleration from force and mass:
Force = 500 N, mass = 25 kg
a = F/m = 500/25 = 20 m/s² (≈ 2.04 g)
Force unit conversion table
| Unit | Symbol | In Newtons | Use case |
|---|---|---|---|
| Newton | N | 1 N | SI base unit; 1 kg·m/s² |
| Kilonewton | kN | 1000 N | Engineering, structural loads |
| Pound-force | lbf | 4.4482 N | Imperial; US engineering |
| Kilogram-force | kgf | 9.8067 N | Everyday weight in metric countries |
| Dyne | dyn | 0.00001 N | CGS system; micro-forces |
| Meganewton | MN | 1,000,000 N | Rocket thrust, large structures |
Real-world force examples
| Object / scenario | Force (N) | Force (kN) |
|---|---|---|
| Ant carrying food | 0.000003 N | 3 × 10⁻⁹ kN |
| Picking up a smartphone | ~1.5 N | 0.0015 kN |
| Human bite force | ~720 N | 0.72 kN |
| Amateur boxer punch | ~500 N | 0.5 kN |
| Pro boxer punch | ~4,000 N | 4 kN |
| Car emergency braking | ~5,000 N | 5 kN |
| Lifting a mid-size car | ~15,000 N | 15 kN |
| Formula 1 downforce at speed | ~18,000 N | 18 kN |
| Elephant body weight | ~50,000 N | 50 kN |
| SpaceX Falcon 9 thrust | 7,607,000 N | 7,607 kN |
| Saturn V launch thrust | 34,020,000 N | 34,020 kN |
Types of Force — Weight, Friction, Centripetal, Impulse & Gravitation
Weight force calculator — W = mg
Weight is the gravitational force acting on a mass. It is not the same as mass. Mass (kg) is the amount of matter; weight (N) is the force due to gravity. On Earth, g = 9.80665 m/s². A 70 kg person weighs 686.5 N on Earth but only 113.8 N on the Moon (g = 1.625 m/s²).
Example: 70 kg person on Earth: W = 70 × 9.807 = 686.5 N
Same person on Moon: W = 70 × 1.625 = 113.8 N
Same person on Jupiter: W = 70 × 24.79 = 1735.3 N
Friction force calculator — f = μN
Friction is a resistive force that opposes relative motion between surfaces. The friction force equals the coefficient of friction (μ) times the normal force (N). There are two types: static friction (prevents motion from starting) and kinetic friction (opposes motion already occurring). Static μ is always higher than kinetic μ for the same surfaces.
Typical μ values (static/kinetic):
Ice–ice: 0.05 / 0.03
Wood–wood: 0.50 / 0.30
Rubber–asphalt: 0.80 / 0.70
Steel–steel: 0.15 / 0.12
Rubber–concrete: 0.90 / 0.80
Example: 20 kg box on wood floor (μ = 0.3):
N = mg = 20 × 9.807 = 196.1 N
f = 0.3 × 196.1 = 58.8 N
Centripetal force calculator — Fc = mv²/r
Centripetal force is the net force directed toward the centre of a circular path that keeps an object moving in a circle. It is not an additional force — it is the result of other forces (friction, tension, gravity, normal force). Formula: Fc = mv²/r, where m is mass, v is speed, and r is the radius of the circular path.
Example: 1200 kg car taking a 40 m radius turn at 15 m/s:
Fc = 1200 × 225 / 40 = 6750 N
This must be provided by tyre–road friction.
Earth orbiting Sun: Fc = GMm/r² = mv²/r
v = √(GM/r) = 29,800 m/s
Impulse calculator — J = FΔt = mΔv
Impulse is the product of force and time, equal to the change in momentum. J = F × Δt = Δp = m × Δv. Measured in N·s (= kg·m/s). Impulse explains why airbags reduce injury (same momentum change, longer time = smaller force), and why batting stance widens during a swing (longer contact time = greater impulse).
Example: Cricket ball (m=0.156 kg) hit from 0 to 40 m/s in 0.002 s:
J = 0.156 × 40 = 6.24 N·s
F = J / Δt = 6.24 / 0.002 = 3120 N
Universal gravitation — F = Gm₁m₂/r²
Newton’s law of universal gravitation: every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. G = 6.674 × 10⁻¹¹ N·m²/kg².
G = 6.674 × 10⁻¹¹ N·m²/kg²
Earth-Moon gravitational force:
m₁ = 5.97 × 10²⁴ kg, m₂ = 7.34 × 10²² kg, r = 3.84 × 10⁸ m
F = 6.674휐⁻¹¹ × 5.97휐²⁴ × 7.34휐²² / (3.84휐⁸)²
F ≈ 1.98 × 10²⁰ N
LazyTools vs Other Force Calculators
| Feature | LazyTools | Omni Calculator | CalculatorSoup | Calculator.io |
|---|---|---|---|---|
| Number of physics modes | ✅ 6 modes | ⚠ 1–2 modes | ⚠ 1 mode (F=ma) | ⚠ 1 mode |
| Bidirectional solve (any variable) | ✅ All modes | ✅ Yes | ✅ Yes | ⚠ Partial |
| Planetary gravity (Moon, Mars...) | ✅ 7 planets | ⚠ Separate tool | ❌ No | ❌ No |
| Full unit conversion | ✅ kg/g/lb/slug, N/kN/lbf/kgf/dyn | ✅ Yes | ⚠ Basic | ⚠ Basic |
| Free body diagram | ✅ SVG, auto-generated | ❌ No | ❌ No | ❌ No |
| Real-world force context | ✅ Auto log-sorted | ❌ No | ❌ No | ❌ No |
| Step-by-step working | ✅ Every result | ❌ No | ❌ No | ⚠ Partial |
| No account required | ✅ Yes | ✅ Yes | ✅ Yes | ✅ Yes |
Force Calculator FAQ
F = m × a. Force (N) = mass (kg) × acceleration (m/s²). Rearranged: a = F/m, m = F/a. 1 Newton = force needed to accelerate 1 kg at 1 m/s².
Multiply: F = m × a. Example: 5 kg at 3 m/s² = 15 N. Enter mass and acceleration in the F=ma tab above, leave F blank.
a = F / m. Example: 1000 kg car, 4000 N force: a = 4000/1000 = 4 m/s² ≈ 0.41 g. Enter F and m, leave a blank.
W = m × g. On Earth g = 9.807 m/s². A 70 kg person weighs 686.5 N on Earth, 113.8 N on Moon, 1735 N on Jupiter. The Weight tab above lets you select any planet.
f = μ × N. Example: 10 kg box, μ = 0.3, N = mg = 98.1 N: f = 0.3 × 98.1 = 29.4 N. Use the Friction tab to solve for f, μ, or N.
Fc = mv²/r. The force directed toward the centre of a circular path. Example: 1000 kg car in 50 m radius turn at 20 m/s: Fc = 1000×400/50 = 8000 N.
J = F × Δt = m × Δv. Change in momentum. Units: N·s. Airbags work by increasing Δt, reducing F. 0.5 kg ball from 0 to 30 m/s: J = 15 N·s.
F = G×m₁×m₂/r². G = 6.674휐⁻¹¹ N·m²/kg². Earth-Moon force: 1.98휐²⁰ N. Use the Gravitation tab for any two masses and distance.
Mass (kg) = amount of matter, constant everywhere. Weight (N) = gravitational force = mg, varies with planet. You weigh 6x less on the Moon but your mass never changes.
Add all forces as vectors. Same direction: add magnitudes. Opposite directions: subtract. Example: 200 N push, 50 N friction = 150 N net force. F_net = ma uses net force.
Enter any 2 of F, m, a in the F=ma tab above. All units supported. Step-by-step working shown. Free body diagram generated. Real-world context shown. Free, no account.
1st: Inertia — objects resist change in motion (ΣF=0 means a=0). 2nd: F=ma — net force = mass × acceleration. 3rd: Action-reaction — forces come in equal, opposite pairs on different objects.
SI unit: Newton (N) = kg·m/s². Also: kN (1000 N), lbf (4.448 N), kgf (9.807 N), dyn (0.00001 N). The calculator converts between all these automatically.
f = μ × N. Doubling μ doubles friction. Ice: μ ≈ 0.03. Asphalt: μ ≈ 0.7. Static μ > kinetic μ — harder to start motion than maintain it.
g-force = a / 9.807. 1 g = 9.807 m/s². Free fall = 1 g. Sports car 0–100 kmh in 3s ≈ 0.94 g. F-16 pull-up ≈ 9 g. Formula 1 braking ≈ 5 g. The F=ma calculator shows g-force for every acceleration result.
m = F / a. Enter F and a in the F=ma tab, leave m blank. Example: 300 N at 6 m/s² = 50 kg.