Newton's Second Law Calculator
Apply F = ma in any unit system, add several forces into a net force for a car, rocket or elevator, and convert a mass to weight on other worlds.
🚀 What is Newton's Second Law?
Newton's second law of motion connects force, mass and acceleration. It says that the net force acting on an object equals its mass times its acceleration, F = m a, and that the acceleration points in the same direction as the net force. Push twice as hard on the same object and it accelerates twice as fast. Push the same way on an object with twice the mass and it accelerates half as fast. The law is the working tool of mechanics: it turns a list of forces into a prediction of how an object will move, and it turns a measured motion back into the force that caused it. This page solves it for whichever of the three quantities you do not know, and it is built around units and scenarios rather than a bare formula.
Because real problems arrive in mixed units, each box has its own unit selector. Force can be entered in newtons, kilonewtons, pound-force, dynes or kilogram-force, mass in kilograms, grams or pounds, and acceleration in m/s squared, in multiples of g, or in ft/s squared. The result is always shown in the unit you chose plus the full set of equivalents, so an engineer working in lbf and a student working in newtons can read the same answer. The scenario presets for a car pulling away, a rocket after liftoff and an elevator passenger fill the boxes with realistic numbers so you can see what a 4500 N force or a 2 g acceleration looks like before you enter your own. For a plain three-tab version in SI units see the force calculator.
The key phrase in the law is net force. A rocket on the pad has a huge thrust and no acceleration, because its weight cancels it. An elevator cable pulling 9500 N on an 800 kg car gives only the difference between the cable force and the 7845 N weight. The Several forces mode does that bookkeeping: enter up to four signed forces, tick whether the weight counts, and it returns the net force, the acceleration in m/s squared and in g, and a chart of how the acceleration would change with mass. To add forces at angles in a plane use the net force calculator, and for motion once you have the acceleration use the acceleration calculator.
Weight is the best-known special case. Weight is the gravitational force on an object, W = m g, which is Newton's second law with the acceleration of free fall. Mass does not change from place to place, but weight does. The Weight mode compares your mass on Earth, the Moon, Mars and Venus, or for any g you type. A few misconceptions are worth clearing up. Force is not needed to keep an object moving at constant velocity, only to change it. A pound-mass is not a pound-force. And a g-force is an acceleration, not a force in newtons. When a support pushes back on an object, see the normal force calculator.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — A Car Pulling Away
A 1500 kg car accelerates at 3 m/s²
Example 2 — A Rocket After Liftoff
A net force of 1000 kN acts on a 50,000 kg rocket, with the answer in g
Example 3 — Mass From Imperial Units
A force of 100 lbf gives an acceleration of 5 ft/s²
Example 4 — An Elevator Accelerating Upward
A cable pulls up with 9500 N on an 800 kg elevator car, weight included
Example 5 — A Car With Drag
A 1500 kg car with 3500 N of drive force, 600 N of air drag and 250 N of rolling resistance on a level road
Example 6 — Weight on the Moon
An astronaut with a mass of 70 kg on the Moon, where g is 1.62 m/s²
❓ Frequently Asked Questions
🔗 Related Calculators
What is Newton's second law?
Newton's second law says the acceleration of an object is directly proportional to the net force on it and inversely proportional to its mass: F = m a. A 1500 kg car accelerating at 3 m/s squared needs a net force of 4500 N.
How do you calculate force from mass and acceleration?
Multiply the mass in kilograms by the acceleration in metres per second squared. The product is in newtons. For 1500 kg and 3 m/s squared the net force is 4500 N, which is 1011.64 lbf.
How do you find acceleration from force and mass?
Divide the net force by the mass: a = F / m. A net force of 1,000,000 N on a 50,000 kg rocket gives 20 m/s squared, about 2.04 g. The acceleration points in the direction of the net force.
How do you find mass from force and acceleration?
Divide the force by the acceleration: m = F / a. A 100 lbf force producing 5 ft/s squared acts on 291.88 kg, which is 20 slugs or about 643.48 lb. Force and acceleration must have the same sign.
What is the difference between a newton, a dyne and a pound-force?
One newton is 1 kg m/s squared. One dyne is 0.00001 N, the CGS unit of force. One pound-force is 4.44822 N, the force that gives a pound-mass the standard gravity. One kilogram-force is 9.80665 N.
Is F in F = ma the net force?
Yes. F is the vector sum of every force on the object. A 800 kg elevator pulled up by a 9500 N cable also has a 7845.32 N weight, so the net force is 1654.68 N and the acceleration is 2.068 m/s squared.
How is weight related to Newton's second law?
Weight is the force of gravity, W = m g, which is the second law with the free-fall acceleration g. A 70 kg person weighs 686.47 N on Earth with g = 9.80665 m/s squared and 113.40 N on the Moon.
What is a g-force?
A g-force is acceleration expressed in multiples of standard gravity, 9.80665 m/s squared. An acceleration of 20 m/s squared is 2.039 g. It is a measure of acceleration, not a force in newtons.
Why does the same force give a lighter object more acceleration?
Because acceleration is force divided by mass. For a fixed force the acceleration falls as 1/m, so doubling the mass halves the acceleration. The chart on this page shows that hyperbola for your numbers.
What happens when the net force is zero?
Then the acceleration is zero and the velocity does not change. The object stays at rest or moves at constant velocity. In net force mode the forces cancel when the sum of applied forces equals the weight.