Solve for Force (F), Mass (m), or Acceleration (a) using F = m · a. Change any value to recalculate instantly, with full unit conversion and a step-by-step walkthrough.
Calculated Force
98N
How is this calculated?
F = m · a
1. Mass in SI: 10 kg = 10 kg
2. Acceleration in SI: 9.8 mps2 = 9.8 m/s²
3. Force = mass × acceleration = 98 N
Guess the force before revealing how close you were.
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About the Newton's Second Law Calculator
Newton's second law of motion states that the net force acting on an object equals its mass multiplied by its acceleration, a relationship written F = ma that is arguably the most consequential equation in classical physics. It is the bridge between the causes of motion and motion itself: forces are the input, acceleration is the output, and mass is the constant of proportionality describing how strongly an object resists being accelerated. Two subtleties matter enormously in practice. The first is that the F in the equation is the net force, the vector sum of every force acting, not any single one — which is why an object can have huge forces on it and no acceleration at all if they cancel. The second is that mass here is inertial mass, a measure of resistance to acceleration, which is conceptually distinct from weight even though the two are routinely conflated in everyday language.
Mathematical Formula & Logic
Newton's second law relates net force, mass and acceleration.
1. The standard form:
F_net = m · a
Where F is net force in newtons, m is mass in kilograms, and a is
acceleration in metres per second squared.
2. Rearrangements:
a = F_net / m
m = F_net / a
3. The general form (valid when mass changes, e.g. a rocket):
F_net = dp/dt
Where p = m·v is momentum. When mass is constant this reduces to F = ma.
4. Net force as a vector sum:
F_net = ΣF = F₁ + F₂ + ... + Fₙ
Forces must be summed as vectors, component by component.
5. Weight as a special case:
W = m · g, where g = 9.80665 m/s² (standard gravity)
6. Definition of the newton:
1 N = 1 kg·m/s²
One newton accelerates one kilogram at one metre per second squared.
Step-by-Step Example
A 1,200 kg car experiences 4,800 N of forward drive force while drag and rolling resistance oppose it with 1,200 N. Find the acceleration:
Step 1 — find the net force, not just the applied force
1. Forward force = +4,800 N
2. Resistive forces = −1,200 N
3. F_net = 4,800 − 1,200 = 3,600 N
Step 2 — apply the second law
4. a = F_net / m = 3,600 / 1,200 = 3.0 m/s²
Step 3 — interpret the result
5. The car gains 3 metres per second of velocity every second.
6. Reaching 100 km/h (27.78 m/s) from rest would take 27.78 / 3.0 = 9.3 s, assuming the forces stayed constant. In reality drag rises with the square of speed, so real acceleration falls off as the car speeds up.
The common mistake
7. Using the 4,800 N drive force alone gives a = 4,800 / 1,200 = 4.0 m/s², overstating the acceleration by a third. The second law takes the net force, so every opposing force must be subtracted first.
Checking the weight for comparison
8. The car's weight is W = m·g = 1,200 × 9.80665 = 11,768 N, which is the downward force gravity exerts on it — a quantity entirely separate from the 3,600 N net horizontal force driving its acceleration.
Reference Data & Values
net force_N
mass kg
acceleration m_s2
1,200
1,200
1.0
3,600
1,200
3.0
7,200
1,200
6.0
3,600
600
6.0
3,600
2,400
1.5
10
2
5.0
Frequently Asked Questions
One newton is the force required to accelerate a mass of one kilogram at one metre per second squared, so it is a derived unit equal to 1 kg·m/s². For a physical sense of scale, holding a small apple of roughly 100 grams against gravity takes about 0.98 N, which is why the newton is sometimes described informally as about the weight of an apple. Structural and automotive work uses kilonewtons because forces at that scale run into the thousands.
Mass is the amount of matter in an object and its resistance to acceleration, measured in kilograms and unchanged by location. Weight is the gravitational force acting on that mass, measured in newtons and dependent on local gravity. A 70 kg person has a mass of 70 kg everywhere but weighs about 686 N on Earth and roughly 114 N on the Moon. Everyday language treats the two as interchangeable because bathroom scales measure force and display mass, silently assuming Earth's gravity.
Because acceleration responds to the vector sum of every force acting, not to any one of them in isolation. A car with 4,800 N of drive force facing 1,200 N of drag accelerates according to the 3,600 N difference, so using the drive force alone overstates the result by a third. This is also why a book resting on a table does not accelerate despite gravity pulling it down: the table's normal force exactly cancels the weight, leaving a net force of zero.
The acceleration is zero, which means the velocity does not change — but that is not the same as the object being at rest. A body already moving continues at constant velocity in a straight line indefinitely, which is Newton's first law and is really a special case of the second. A car cruising at a steady motorway speed has zero net force because drive force exactly balances drag and rolling resistance, and an aircraft in level flight at constant speed is in the same condition.
Not directly. The simple form assumes constant mass, so it fails for systems like rockets that expel a substantial fraction of their mass as propellant. The general form of the second law is F = dp/dt, the rate of change of momentum, which correctly handles varying mass and reduces to F = ma when mass is constant. Rocket motion is analysed with the Tsiolkovsky rocket equation, which follows from the momentum form rather than the familiar one.
The first law is the zero-force case of the second: with no net force there is no acceleration, so an object at rest stays at rest and one in motion continues at constant velocity. The third law states that forces come in equal and opposite pairs acting on different bodies, which is what lets you identify all the forces that must be summed to obtain the net force in the second law. Together the three describe how forces arise, how they combine, and what motion results.