Newton's second law links force, mass and acceleration. Enter a mass and an acceleration to get the net force in newtons, along with the object's weight on Earth.
Enter the mass in kilograms.
Enter the acceleration in m/s².
Read the force and weight.
Force: F = m × a
Weight: W = m × g
This calculator applies Newton's second law, F = ma. Enter a mass in kilograms and an acceleration in m/s², and it gives the net force in newtons needed to produce that acceleration. It also shows the object's weight on Earth, mg, so you can compare the force you are working with against the pull of gravity on the same mass.
Students meet F = ma in Class 9 and use it throughout Class 11 mechanics. Engineers use it to size motors, brakes and supports. It answers questions such as how hard a car's tyres must push to reach a given acceleration, or what force a lift cable carries when the lift speeds up. The key word is net: the formula gives the total of all forces acting, not any single one.
1. Write the mass in kilograms. Convert grams by dividing by 1000 and tonnes by multiplying by 1000.
2. Write the acceleration in m/s². If you know a change in speed over a time, use a = (v − u) ÷ t.
3. Multiply: F = m × a. The answer is in newtons, where 1 N = 1 kg·m/s².
4. Give the force the same sign as the acceleration. A negative value means the net force points opposite to your chosen positive direction.
5. For weight, multiply the mass by g = 9.81 m/s²: W = m × g.
6. If other forces act, such as friction, remember that F is their vector sum, not the applied force alone.
In its general form the law says the net force equals the rate of change of momentum, F = dp/dt. When mass is constant, p = mv, so dp/dt = m dv/dt = ma. This is why F = ma fails for rockets, whose mass drops as fuel burns. The law defines the newton: the force that gives 1 kg an acceleration of 1 m/s². Mass here is inertial mass, the resistance of a body to having its motion changed.
If a 1200 kg car accelerates at 3 m/s², the net force is 3600 N. The engine's driving force at the tyres is larger, because air drag and rolling resistance push back. So you draw a free-body diagram, add all forces with their directions, and set the total equal to ma. When the acceleration is zero, the forces are balanced. The body may still be moving at a constant velocity, which is Newton's first law as a special case of the second.
Weight is the gravitational force on a body, W = mg. The calculator uses g = 9.81 m/s², a standard average for the Earth's surface. The real value varies slightly with latitude and altitude, about 9.78 at the equator and 9.83 at the poles. Mass does not change from place to place, but weight does: a 60 kg person weighs about 589 N on Earth and only about 97 N on the Moon, where g is about 1.62 m/s².
A loaded autorickshaw of mass 650 kg picks up speed at a steady 1.8 m/s² as it pulls away from a stand in Pune.
Newton's second law: F = m × a = 650 × 1.8 = 1,170 N
Weight on Earth: W = m × g = 650 × 9.81 = 6,376.5 N
Answer: Force 1,170 N; Weight (on Earth) 6,376.5 N
Entering mass in grams or tonnes instead of kilograms.
Treating the answer as the engine or applied force when friction and drag also act.
Confusing mass in kg with weight in newtons, or quoting weight in kg.
Using F = ma for a system whose mass changes during the motion, such as a rocket.
Dropping the sign of a deceleration and getting a force pointing the wrong way.
Solving Class 9 and Class 11 problems on Newton's laws.
Estimating the braking force needed to stop a vehicle in a given time.
Finding the tension in a lift cable while it accelerates.
Sizing motors and actuators for conveyors and robotic arms.
Comparing weight on Earth with other forces acting on the same object.
Is mass the same as weight?
No. Mass is in kg and stays constant; weight is a force in newtons and depends on gravity.
What about deceleration?
Enter a negative acceleration; the force will be negative, meaning it opposes the motion.