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Force Calculator — Newton’s Second Law

Newton's second law F = m·a, with acceleration in g, time to 100 km/h, and a block that really accelerates beside a velocity-time line.

Newton's second law: F = m·a. Pick which quantity to solve for and enter the other two.

Mass m (kg)Acceleration a (m/s²)

Race against× the mass

4.20 kN

force

Acceleration in g

0.306 g

Weight on Earth

13.73 kN

m × 9.81

0 to 100 km/h

9.26 s

Distance in 1 s

1.50 m

3.00 m/s by then

F = m·a = 1,400 × 3 = 4.20 kN

Momentum added per second4,200 kg·m/s

This force compared with its weight0.306×

Weight on the Moon2.27 kN

Instant insight

4.20 kN on 1,400 kg gives 3 m/s²
F = ma, and the useful rearrangement is a = F/m. Double the force and you double the acceleration; double the mass and you halve it. That is the entire content of the law, and it is why the heavier block in the race below falls behind under an identical arrow.
From rest, that reaches 100 km/h in 9.26 s
And covers 1.50 m in the first second alone — but four times that in the first two, because distance goes as t² while speed goes as t. The block on screen shows it: equal time marks with unequal gaps.
That is 0.31 g
Less than gravity. Holding this mass up against its own weight would take 13.73 kN — 3.3 times the force you are applying.
Mass in kilograms, weight in newtons — they are not the same thing
This 1,400 kg mass weighs 13.73 kN on Earth and would weigh 2.27 kN on the Moon, but its mass — and therefore how hard it is to accelerate — is identical in both places. A bathroom scale measures weight and prints mass, which is where most of the confusion starts.
Force is really the rate of change of momentum
F = ma is the special case for constant mass. What Newton wrote was F = dp/dt, and this force adds 4,200 kg·m/s of momentum every second. The general form is what you need for a rocket, which loses mass as it burns, and it is the same statement as the impulse–momentum theorem.
What the model leaves out
A single constant force on a constant mass in one dimension, with no friction, no drag and no rotation. A real net force is the sum of everything acting — including the friction and air resistance that make an actual object settle at a terminal speed rather than accelerating forever.

Worked out in your browser — nothing is sent anywhere.

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Everyday Uses

Solving F = ma for any unknown

Solve for force, mass or acceleration when you know the other two.

Braking and impact

Work out the force involved in bringing a moving mass to a stop.

Structural loads

Convert a mass in kilograms into the weight force a support must carry.

Different gravity

See how the same mass weighs differently on the Moon or Mars.

Feeling heavy in a lift

As a lift accelerates upward the floor pushes harder than your weight alone, and on the way down it pushes less. Put the acceleration in and you get the reading a bathroom scale would show.

Rope, anchor and bracket ratings

A load that is being accelerated or arrested pulls harder than its static weight. Kit rated only for the standing load is the usual reason a fixing fails.

Frequently Asked Questions

How does this relate to Newton's second law?

It is Newton's second law, stated as F = ma: the net force on an object equals its mass multiplied by its acceleration. Rearranged, a = F/m tells you how fast something speeds up under a known push, and m = F/a gives mass from a measured force and acceleration. The law only applies to the net force — the vector sum of everything acting on the object — so competing forces have to be resolved first. Where the net force is zero the acceleration is zero, which is Newton's first law falling out as a special case.

What is Newton's second law?

Force equals mass times acceleration — F = ma. A newton is the force that accelerates one kilogram at one metre per second squared. The law is why the same push moves a shopping trolley easily and a car barely at all: for a given force, acceleration falls as mass rises. It also means force is required to *change* motion, not to maintain it, which is the part that contradicts everyday intuition.

What is the difference between mass and weight?

Mass is how much matter an object contains, measured in kilograms, and it does not change with location. Weight is the force gravity exerts on that mass — mass times gravitational acceleration — measured in newtons. A 70 kg person weighs about 686 N on Earth but roughly 113 N on the Moon, while their mass is 70 kg in both places. Bathroom scales report mass but are calibrated assuming Earth's gravity.

Why is the newton such a small unit?

Because one newton is only about the weight of a small apple — 102 grams. Everyday forces are therefore large numbers: a 70 kg person standing still exerts 686 N on the floor, and a car braking hard generates several thousand. Engineers commonly work in kilonewtons for structural loads. The unit is small because it derives from base SI units rather than from anything human-scaled.

How do multiple forces combine?

As vectors, not simple sums. Two forces in the same direction add; opposing forces subtract; forces at an angle combine using components or the parallelogram rule. The net force determines the acceleration. This is why an object can have several large forces acting on it and not accelerate at all — a book on a table has gravity pulling down and the table pushing up in balance, netting zero.

What is the relationship between force, impulse and momentum?

Force applied over time changes momentum, and that product is impulse. The same change in momentum can come from a large force briefly or a small force for longer — which is the entire principle behind crumple zones, airbags and landing with bent knees. They extend the stopping time, reducing the peak force for the same overall change in motion.

Does F = ma always hold?

For everyday situations, yes. It breaks down at speeds approaching light, where relativistic mass increase means force produces less acceleration than expected, and at atomic scales where quantum mechanics governs. It also assumes constant mass — a rocket burning fuel loses mass as it accelerates, so the more general form uses rate of change of momentum instead. For anything you can push by hand, F = ma is exact enough.