Acceleration, Force and Mass Calculator
This calculator applies Newton's second law of motion: Force = mass times acceleration. Pick which variable you want to find, enter the other two, and the result updates instantly. Switch units between metric and imperial, follow the step-by-step working panel to see exactly how the answer was reached, and check the reference table for real-world acceleration examples.
Formula
Worked example
A 10 kg shopping trolley is pushed with a net force of 100 N. Using a = F / m: a = 100 / 10 = 10 m/s². That is roughly 1.02 g, a brisk but comfortable acceleration.
Newton's second law: the physics behind this calculator
Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The relationship is expressed as F = m * a, where F is the net force in Newtons, m is the mass in kilograms, and a is the acceleration in metres per second squared. A larger force produces a larger acceleration for the same mass, while a heavier object needs more force to achieve the same acceleration. This is why a feather and a bowling ball fall identically in a vacuum but very differently in air: in air, drag (a force) acts differently on each object.
How to use this calculator: three solve modes
The calculator can solve for any one of the three variables in F = ma. Select which variable you want to find from the Solve for drop-down, enter the other two values, and the result appears instantly. Use the unit selectors beside each input to work in any combination of Newtons, kilonewtons, pound-force, or kilogram-force for force; kilograms, grams, pounds, or ounces for mass; and m/s², cm/s², ft/s², or g for acceleration. The steps panel below the result walks through the arithmetic with your actual numbers so you can check every conversion.
Unit conversions and the g-force output
Acceleration is often expressed in multiples of standard gravity, abbreviated g or g-force, where 1 g = 9.80665 m/s². This unit is convenient because it describes how much extra weight an object or person appears to gain: at 2 g you feel twice your normal body weight pressing you into your seat. This calculator always shows the result in m/s² (the SI unit) and also converts it to g automatically. Force is given in Newtons and also in kilogram-force and pound-force, so the result can be compared directly with values in different textbooks or engineering references.
Net force, friction and real-world applications
The F in F = ma is always the net (resultant) force: the vector sum of every force acting on the object. In real situations this usually means subtracting friction, air drag, or gravitational components. For example, if a 1 000 kg car engine produces 4 000 N of thrust but friction and drag total 1 000 N, the net force is 3 000 N and the acceleration is 3 m/s². To use this calculator for a real scenario, add up all the forces and enter their resultant. If the net force is zero, Newton's first law takes over: the object moves at constant velocity or stays at rest.
Real-world acceleration reference
| Scenario | Approx. acceleration (m/s²) | Approx. g-force | Notes |
|---|---|---|---|
| Falling leaf | 0.1-0.5 | 0.01-0.05 g | Air drag limits acceleration |
| Gentle car start | 1-2 | 0.1-0.2 g | Comfortable for passengers |
| Braking hard (car) | 7-9 | 0.7-0.9 g | Near the friction limit on dry tarmac |
| Free fall (Earth) | 9.81 | 1 g | Standard gravity, no air resistance |
| Sports car 0-100 km/h | 7-12 | 0.7-1.2 g | Best production cars ~0-4 s |
| Roller-coaster peak | 20-40 | 2-4 g | Brief peaks on major rides |
| Fighter jet maneuver | 49-88 | 5-9 g | Requires G-suit above 4-5 g |
| Rocket launch | 29-49 | 3-5 g | Astronauts experience 3-5 g at max-q |
| Car crash (airbag) | 200-500 | 20-50 g | Millisecond duration; survivable |
| Bullet in barrel | 3000-9000 | 300-900 g | Very short duration |
Typical peak accelerations for common scenarios, expressed in both m/s² and multiples of g (1 g = 9.80665 m/s²).
Frequently asked questions
What is Newton's second law?
Newton's second law states that the net force on an object equals its mass multiplied by its acceleration: F = m * a. It means that applying a larger force to the same object produces proportionally more acceleration, and that a heavier object requires proportionally more force to achieve the same acceleration. This law is the foundation of classical mechanics and underlies everything from car-crash engineering to rocket propulsion.
What is the unit of acceleration?
The SI unit of acceleration is metres per second squared (m/s²). It means that for every second the force is applied, the object's velocity increases by that many metres per second. Acceleration is also commonly expressed in g-force, where 1 g = 9.80665 m/s² (the standard gravitational acceleration at Earth's surface). Other common units include feet per second squared (ft/s²) and centimetres per second squared (cm/s²).
What is a Newton?
A Newton (N) is the SI unit of force. One Newton is the force needed to accelerate exactly 1 kilogram of mass at 1 m/s². It is equivalent to about 0.2248 pound-force or 0.1020 kilogram-force. The unit is named after Sir Isaac Newton in recognition of his formulation of classical mechanics.
How do I calculate acceleration from force and mass?
Divide the net force (in Newtons) by the mass (in kilograms). If a 5 kg object experiences a net force of 20 N, the acceleration is 20 / 5 = 4 m/s². Make sure you use the net force, not just the applied force, because friction and other opposing forces reduce the effective force available to accelerate the object.
What if the force and acceleration are in different unit systems?
Convert everything to SI units first: Newtons for force and kilograms for mass. The unit selectors in this calculator handle the conversions automatically. For example, if the force is in pound-force (lbf) and the mass is in pounds (lb), the calculator converts both to Newtons and kilograms before applying F = ma, then converts the result back to the unit you prefer.
What is the difference between weight and mass?
Mass is the amount of matter in an object and does not change with location (on the Moon you have the same mass as on Earth). Weight is the gravitational force acting on that mass: W = m * g, where g is local gravitational acceleration (9.81 m/s² at Earth surface, 1.62 m/s² on the Moon). A 70 kg person weighs 686 N on Earth but only 113 N on the Moon, while their mass stays 70 kg throughout.
How many g-forces can a human body withstand?
Trained fighter pilots in a G-suit can briefly sustain 9 g in the direction that pushes blood toward the feet (the most dangerous direction). Untrained people typically lose consciousness at 4-5 g. In the chest-to-back direction (as during rocket launches), humans can tolerate higher g-forces for short periods - astronauts routinely experience 3-5 g during launch. Very brief impulsive forces, like an airbag deploying, can exceed 50 g without causing fatal injury because the duration is milliseconds.