Calculate force, mass, or acceleration using Newton's Second Law F = ma. Convert results between Newtons, kilonewtons, pounds-force, and dynes. Also includes weight force and friction force calculators for complete physics problem solving.
✓Last verified: April 2026 · NIST & Physics Classroom sourced
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kg
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m/s²
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N
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kg
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m/s²
Used only when Custom gravity is selected
kg
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Please enter friction coefficient.
Dimensionless (typically 0.1 to 1.0)
Force
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Sources & Methodology
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Force formulas and unit conversion factors verified against NIST standards, The Physics Classroom, and Engineering Toolbox reference tables.
The National Institute of Standards and Technology (NIST) is the US authority on measurement standards. All force unit conversion factors used in this calculator — Newtons to pounds-force (1 lbf = 4.44822 N), Newtons to dynes (1 N = 100,000 dyn), and kilogram-force (1 kgf = 9.80665 N) — are sourced from official NIST publications for maximum accuracy.
The Physics Classroom provides comprehensive, peer-reviewed physics education resources used by millions of students and educators worldwide. The F = ma formulation, mass and acceleration unit conversions, and worked examples in this calculator are verified against Physics Classroom's treatment of Newton's Second Law and its applications.
The friction coefficient reference values (rubber on concrete 0.7, steel on steel 0.5, ice on ice 0.15, etc.) in this calculator's friction force tab are sourced from Engineering Toolbox's widely-cited table of static and kinetic friction coefficients for common material pairs.
Methodology: F = ma — Newton's Second Law. All mass inputs are converted to kilograms before calculation (1 lb = 0.453592 kg, 1 slug = 14.5939 kg, 1 g = 0.001 kg, 1 t = 1000 kg). All acceleration inputs are converted to m/s squared (1 ft/s squared = 0.3048 m/s squared, 1g = 9.80665 m/s squared). Results in Newtons are then converted to kN (divide by 1000), lbf (divide by 4.44822), dyn (multiply by 100000), and kgf (divide by 9.80665). Friction force = mu x (mass x 9.80665). Weight force = mass x gravitational acceleration.
⏱ Last reviewed: April 2026
How to Calculate Force — Newton's Second Law Explained
Force is one of the most fundamental concepts in physics and engineering. Every push, pull, gravity, friction, tension, and pressure is a force. Newton's Second Law of Motion — F = ma — gives us the precise mathematical relationship between force, mass, and acceleration. This single equation underlies everything from launching rockets to designing car brakes, from calculating structural loads to understanding why heavier objects are harder to move.
The Force Formula: F = ma
Newton's Second Law states that the net force acting on an object equals the product of its mass and acceleration. The direction of acceleration is always the same as the direction of the net force.
F = m x a
F = Force (Newtons, N) — what you want to find m = Mass (kilograms, kg) — resistance to acceleration a = Acceleration (m/s²) — rate of change of velocity
Rearranged forms:
m = F / a (find mass from force and acceleration)
a = F / m (find acceleration from force and mass)
Example: A 1,500 kg car accelerates at 3 m/s²:
F = 1,500 x 3 = 4,500 N = 4.5 kN = 1,011 lbf
Force Units and Conversions
The SI unit of force is the Newton (N), defined as the force required to accelerate a 1 kg mass at 1 m/s². In the imperial system, the pound-force (lbf) is standard. The CGS system uses the dyne. Engineering contexts also use the kilonewton (kN) for large forces and kilogram-force (kgf) for loads compared to weight.
Unit
Symbol
Equivalence
Common Use
Newton
N
1 kg·m/s²
SI standard, all physics
Kilonewton
kN
1,000 N
Structural engineering, bridges
Pound-force
lbf
4.44822 N
US engineering, aircraft
Dyne
dyn
0.00001 N
CGS system, small forces
Kilogram-force
kgf
9.80665 N
Weight specifications
Meganewton
MN
1,000,000 N
Rocket thrust, large structures
Weight Force — Gravity as a Force
Weight is the most familiar force in everyday life — it is simply the gravitational force acting on a mass. Weight is not the same as mass. Mass (in kg) is an intrinsic property of matter; weight (in N) depends on the gravitational field you are in. On Earth, the standard gravitational acceleration is g = 9.80665 m/s². The weight of a 70 kg person is 70 x 9.80665 = 686.5 N = 154.3 lbf.
On the Moon (g = 1.62 m/s²), that same 70 kg person weighs only 70 x 1.62 = 113.4 N — about one-sixth their Earth weight. On Mars (g = 3.72 m/s²), they would weigh 260.4 N. The mass stays constant at 70 kg regardless of location; only the weight (force) changes.
Friction Force
Friction force is the resistive force that opposes relative motion between two surfaces in contact. It is calculated as the product of the coefficient of friction (mu) and the normal force (the perpendicular contact force, which equals weight for a horizontal surface). Understanding friction is essential for calculating stopping distances, designing brakes, analyzing conveyor systems, and solving inclined plane problems.
Friction Force (Ff) = mu x Normal Force (N)
On a flat surface: Normal Force = Weight = mass x 9.80665
So: Ff = mu x mass x 9.80665
Example: A 30 kg box on a wooden floor (mu = 0.30):
Normal Force = 30 x 9.80665 = 294.2 N
Friction Force = 0.30 x 294.2 = 88.3 N = 19.8 lbf
This is the minimum force needed to start sliding the box.
💡 Static vs Kinetic Friction: The coefficient of friction has two values: static friction (higher, prevents initial motion) and kinetic friction (lower, opposes ongoing sliding). Engineering Toolbox and most references list static coefficients. Kinetic coefficients are typically 10-25% lower. For example, rubber on dry concrete: static mu = 0.80, kinetic mu = 0.65. Use static mu to find the force needed to start motion; use kinetic mu for forces during sliding.
Frequently Asked Questions
The formula for force is F = m x a (Newton's Second Law), where F is force in Newtons, m is mass in kilograms, and a is acceleration in m/s squared. You can rearrange it to find mass: m = F / a, or acceleration: a = F / m. This single equation governs all classical mechanics problems involving force.
Multiply mass in kilograms by acceleration in m/s squared. For example, a 10 kg object accelerating at 5 m/s squared has force = 10 x 5 = 50 Newtons. If your mass is in pounds, divide by 2.20462 to convert to kg first. If acceleration is in ft/s squared, multiply by 0.3048 to convert to m/s squared.
Rearrange F = m x a to get m = F / a. Divide force in Newtons by acceleration in m/s squared to get mass in kilograms. For example, a force of 150 N producing 3 m/s squared acceleration means mass = 150 / 3 = 50 kg. Use this to find the mass of an unknown object when you know the applied force and resulting acceleration.
Rearrange F = m x a to get a = F / m. Divide force in Newtons by mass in kilograms to get acceleration in m/s squared. Example: 200 N applied to 40 kg gives a = 200 / 40 = 5 m/s squared. To express as g-force, divide by 9.80665: 5 / 9.80665 = 0.51g.
Multiply Newtons by 0.224809 to get pounds-force (lbf). For example, 500 N x 0.224809 = 112.4 lbf. To convert lbf back to Newtons, multiply by 4.44822. One lbf is the gravitational force on a one-pound mass at standard Earth gravity (9.80665 m/s squared).
Mass is the amount of matter in an object, measured in kilograms — it never changes regardless of location. Weight is the gravitational force on that mass, measured in Newtons, and changes with gravitational field strength. A 70 kg person has a mass of 70 kg everywhere, but weighs 686 N on Earth, 113 N on the Moon, and 19,180 N on the Sun's surface.
Net force is the vector sum of all forces acting on an object. Forces in the same direction are added; opposing forces are subtracted. For example, a 100 N forward push against 30 N of friction gives a net force of 70 N forward. The object then accelerates at a = 70 / mass. If net force = 0, the object is in equilibrium and does not accelerate.
Friction force = coefficient of friction (mu) x Normal force. On a flat horizontal surface, normal force equals weight (mass x 9.80665 N/kg). For example, a 25 kg box on a surface with mu = 0.35: friction = 0.35 x (25 x 9.80665) = 0.35 x 245.2 = 85.8 N. This is the force you must overcome to slide the box.
One pound-force (lbf) equals exactly 4.44822 Newtons. This is an exact defined relationship. To convert any lbf value to Newtons, multiply by 4.44822. To convert Newtons to lbf, multiply by 0.224809. This conversion appears constantly in engineering when switching between US customary and SI specifications.
G-force is acceleration expressed as a multiple of standard gravity (g = 9.80665 m/s squared). g-force = acceleration (m/s squared) / 9.80665. A car braking at 7.85 m/s squared decelerates at 7.85 / 9.80665 = 0.8g. Fighter pilots can sustain 9g briefly. Roller coasters reach about 5g at the bottom of drops. Human blackout typically occurs above 5g sustained.
On an incline at angle theta: the gravitational force component along the slope (pulling object down the slope) = m x g x sin(theta). The normal force (perpendicular to slope) = m x g x cos(theta). Friction force opposing motion up or down the slope = mu x normal force = mu x m x g x cos(theta). For a 40 kg box on a 30 degree slope: force along slope = 40 x 9.80665 x 0.5 = 196.1 N.
SI system: Newton (N) = kg times m/s squared. Imperial: pound-force (lbf), where 1 lbf = 4.44822 N. CGS: dyne, where 100,000 dynes = 1 N. Technical metric: kilogram-force (kgf), where 1 kgf = 9.80665 N. Engineering also uses kilonewton (kN = 1,000 N) and meganewton (MN = 1,000,000 N) for large-scale structural and aerospace applications.