Force Calculator
Enter any two of force, mass and acceleration — the calculator returns the third using Newton’s second law, F = m·a, and converts the force into common units.
Force
98.0665 N
- Force (kilonewtons)
- 0.098066 kN
- Force (pound-force)
- 22.0462 lbf
- Force (kilogram-force)
- 10.0000 kgf
- Force (dyne, CGS)
- 9.8066e+6 dyne
Newton’s second law: F = m·a. One newton accelerates one kilogram at one metre per second squared.
How to use this calculator
Pick what you want to solve for from the dropdown — force (F), mass (m), or acceleration (a). Then fill in the other two quantities. The unused field is ignored, so you can leave its default in place. Use SI units: mass in kilograms (kg), acceleration in metres per second squared (m/s²), and force in newtons (N). Direction is handled by the sign of the number — a negative acceleration means the object is decelerating (or accelerating in the opposite direction), and the calculated force takes the same sign. The default scenario shows the weight of a 10 kg object on Earth (a 10 kg mass under standard gravity, g₀ = 9.806 65 m/s², experiences a downward force of about 98 N).
How the calculation works
Newton’s second law of motion states that the net force on an object equals its mass times its acceleration: F = m·a. The law was first published by Isaac Newton in the 1687 Principia and is one of the foundations of classical mechanics. In SI units a force of one newton is defined as the force that accelerates a one-kilogram mass at one metre per second squared, so 1 N = 1 kg·m/s². Rearranging the equation gives the other two forms: m = F / a (find mass from a known force and acceleration) and a = F / m (find the acceleration produced by a force on a known mass). The law applies only to inertial reference frames and to objects whose mass does not change appreciably during the motion — it is not the right tool for rockets shedding fuel (use Tsiolkovsky’s equation) or for speeds approaching that of light (use special relativity). Force, mass and acceleration are all vector or scalar quantities here, but the calculator works in one dimension along a chosen axis. If you need force components in different directions, run the calculator once per axis.
Worked example
A 1 200 kg car accelerates from rest to 27 m/s (about 60 mph) over 9 seconds. Average acceleration is a = (27 − 0) / 9 = 3 m/s². The driving force the engine must transmit to the wheels (ignoring drag and rolling resistance) is F = m·a = 1 200 × 3 = 3 600 N, or 3.6 kN — roughly 810 lbf. Solving the inverse: a child pushes a 25 kg sledge with 50 N of force on a frictionless ice rink. Acceleration is a = F / m = 50 / 25 = 2 m/s². Both calculations are direct one-line applications of F = m·a; the work is in deciding what counts as the "net" force (after subtracting friction, drag, normal-force components, etc.) before you apply the formula.
Frequently asked questions
What is Newton’s second law?
Newton’s second law of motion says that the net force F acting on an object equals the rate of change of its momentum. For an object of constant mass m and acceleration a, that simplifies to the familiar F = m·a. It was published by Isaac Newton in 1687 in the Principia (Lex II) and is one of three laws that, together with his law of universal gravitation, underpin classical mechanics. The law tells you that bigger forces produce bigger accelerations, and that heavier objects need bigger forces to accelerate at the same rate as lighter ones.
What is a newton (N)?
A newton is the SI unit of force. By definition, one newton is the force that accelerates a one-kilogram mass at one metre per second squared: 1 N = 1 kg·m/s². On Earth, the gravitational pull on a 100-gram apple is roughly one newton — which is how the unit is sometimes remembered. The newton was adopted as the SI unit of force at the 9th General Conference on Weights and Measures (CGPM) in 1948 and named for Isaac Newton.
How do I convert newtons to pounds-force?
One pound-force (lbf) is defined as exactly 4.448 222 newtons (NIST SP 811, 2008). To convert newtons to pound-force, divide by 4.448 222; to go the other way, multiply by 4.448 222. So 100 N ≈ 22.48 lbf, and 50 lbf ≈ 222.4 N. The calculator does this automatically in the breakdown below the primary result.
Is mass the same thing as weight?
No, they are different physical quantities. Mass is the amount of matter in an object, measured in kilograms; it does not depend on where the object is. Weight is a force — the gravitational pull on the object — measured in newtons. On Earth, weight in newtons equals mass in kilograms times the local gravitational acceleration g, which averages about 9.81 m/s² but varies slightly by latitude and altitude. So a 10 kg object has the same mass on the Moon as on Earth, but its weight on the Moon (about 16 N) is only one-sixth of its weight on Earth (about 98 N). This calculator treats mass and force separately, which is the physics-correct distinction.
What is the difference between F = m·a and momentum?
Momentum (p) is the product of mass and velocity: p = m·v. Newton actually stated his second law in terms of momentum — force equals the rate of change of momentum, F = dp/dt. When mass is constant, dp/dt = m·dv/dt = m·a, which gives the familiar F = m·a. When mass changes (a rocket burning fuel, a conveyor belt picking up material), you have to use the full momentum form, because the F = m·a shortcut no longer captures the mass-change term. For everyday problems — cars, balls, sleds, falling apples — mass is effectively constant and F = m·a is exact.
When does F = m·a fail?
In two regimes. First, at speeds close to the speed of light (more than about 10 % of c, roughly 30 000 km/s), Newtonian mechanics is replaced by special relativity, where momentum is γm·v and the relationship between force and acceleration is different. Second, at very small scales (atoms, electrons), classical mechanics is replaced by quantum mechanics, where particles do not have definite trajectories at all. For everything between a falling pencil and a flying jumbo jet, F = m·a is accurate to many decimal places and is the right tool.