Physics calculator
Force Calculator
Solve Newton's second law for force, mass, or acceleration in metric or imperial units, including weight under standard gravity.
Calculated force
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Enter two compatible values to calculate.
What is force?
Force is a push or pull that can change an object's motion. The SI unit of force is the newton (N). This calculator finds force, mass, or acceleration when the other two values are known.
Newton's second law
Newton's second law says that an object's net force equals its mass multiplied by its acceleration:
Force and mass are converted to newtons and kilograms, while acceleration is converted to meters per second squared before calculation.
Force, mass, and acceleration
Force is measured in newtons, mass in kilograms, and acceleration in meters per second squared. Rearranging the equation gives:
A negative acceleration represents acceleration in the opposite direction of the chosen positive direction. Mass cannot be negative.
Worked examples
For a 10 kg object accelerating at 2 m/s²:
For 20 N of force acting on 4 kg:
One kilogram accelerating at standard gravity produces:
Units and conversions
The calculator uses SI units internally. It uses 1 lb = 0.45359237 kg, 1 ft/s² = 0.3048 m/s², standard gravity g = 9.80665 m/s², and 1 lbf = 4.4482216152605 N. A newton and a pound-force are both force units, but they are not numerically equal.
Common uses
Force calculations are useful in mechanics, engineering, vehicle dynamics, structural analysis, sports science, and estimating the load produced when an object accelerates or decelerates.
Frequently asked questions
What is the difference between newtons and pounds-force?
A newton is the SI unit of force. A pound-force is an imperial force unit; 1 lbf equals approximately 4.44822 N.
Can acceleration be negative?
Yes. Negative acceleration indicates a direction opposite to the selected positive direction, so the resulting force can also be negative.
Can mass be zero or negative?
Zero mass can produce zero force, but it cannot be used as a divisor when finding acceleration. Negative mass is rejected because it is not a valid ordinary physical input.
Why is no result shown?
The calculator needs two valid known values. Blank, non-finite, negative-mass, or division-by-zero inputs are not used.
What does standard gravity mean?
Standard gravity is the defined reference acceleration 9.80665 m/s², written as g or g0. It is a reference value, not a promise that gravity is identical everywhere.
How the calculator works
Pick which quantity to solve for, enter the other two, and the calculator applies Newton's second law. Force can be entered or displayed in newtons, kilonewtons, or pounds-force; mass in kilograms, grams, or pounds; and acceleration in m/s², ft/s², or multiples of standard gravity (g). Every input is converted to SI units (N, kg, m/s²) before the math, and the answer is converted back to the unit you selected for the calculated field.
The results panel lists all three quantities plus the force expressed three ways: newtons, kilonewtons, and pounds-force. Mass must be zero or greater, and the calculator will not divide by a zero acceleration or a zero mass. Force and acceleration can be negative, which simply means they point in the opposite direction to the one you chose as positive. Values are shown to six decimal places, with scientific notation for extremely small or large numbers.
The standard gravity option is the quickest way to find weight. Leave acceleration at 1 g (9.80665 m/s²), enter a mass, and the resulting force is that object's weight on Earth.
Newton's second law
F is the net force in newtons, m is mass in kilograms, and a is acceleration in meters per second squared. One newton is the force that gives a 1 kg mass an acceleration of 1 m/s². The two rearranged forms are just the same relationship solved for a different unknown.
Worked example: a 1,200 kg car accelerating at 2.5 m/s² needs a net force of F = 1,200 × 2.5 = 3,000 N, which is 3 kN or about 674.4 lbf (3,000 ÷ 4.4482). Another: the weight of a 70 kg person is 70 × 9.80665 = 686.5 N, or 154.3 lbf, which matches their mass of 154.3 lb because 1 lb of mass weighs exactly 1 lbf under standard gravity.
Units of force, mass, and acceleration
The conversion factors the calculator uses are the internationally agreed exact or standard values:
- 1 newton (N) = 1 kg·m/s²
- 1 kilonewton (kN) = 1,000 N
- 1 pound-force (lbf) = 4.4482216 N
- 1 pound (lb, mass) = 0.45359237 kg
- 1 gram (g) = 0.001 kg
- 1 ft/s² = 0.3048 m/s²
- 1 standard gravity (g) = 9.80665 m/s² = 32.174 ft/s²
Pounds, pounds-force, and weight versus mass
Mass is how much matter an object contains and does not change with location. Weight is the force gravity exerts on that mass, so it is a force and depends on the local gravitational acceleration. A 10 kg mass weighs 98.07 N on Earth but only about 16.2 N on the Moon, where g is roughly 1.62 m/s².
In US customary units the same word is used for both, which causes endless confusion. The pound (lb) in the mass menu is pound-mass, and the pound-force (lbf) in the force menu is the weight of one pound-mass under standard gravity. They are numerically equal only when the acceleration is exactly 1 g. If you enter 10 lb of mass at 2 g, the force is 20 lbf, not 10.
Net force and common mistakes
The F in F = ma is the net force, the vector sum of every force acting on the object. A box pushed with 50 N against 20 N of friction has a net force of 30 N, and it is the 30 N that determines its acceleration. If the forces balance, the net force is zero and the object keeps its current velocity, including staying at rest.
Unit mixing is the usual source of wrong answers. Entering 500 in grams with the menu on kg gives a force a thousand times too large; 500 g accelerating at 2 m/s² is 0.5 × 2 = 1 N, not 1,000 N. A second trap is using weight where mass belongs: a 160 lb person has a mass of 72.6 kg, and it is the kilograms that go into F = ma. Lastly, F = ma is a classical law. It is exact for everyday speeds and fails only near the speed of light or when mass changes during the motion, as with a rocket burning fuel.
Frequently asked questions
What is the formula for force?
Force equals mass times acceleration: F = m × a. With mass in kilograms and acceleration in meters per second squared, the force comes out in newtons.
How do you calculate force from mass and acceleration?
Multiply the two together. A 10 kg object accelerating at 3 m/s² experiences a net force of 10 × 3 = 30 N.
What is a newton?
A newton is the SI unit of force, defined as the force needed to accelerate a 1 kg mass at 1 m/s². It equals about 0.2248 pounds-force, roughly the weight of a small apple.
How do you convert mass to weight?
Multiply the mass by the acceleration due to gravity, 9.80665 m/s² on Earth. A 50 kg mass weighs 50 × 9.80665 = 490.3 N. In the calculator, choose standard gravity as the acceleration unit and enter 1.
Is a pound the same as a pound-force?
No. The pound (lb) is a unit of mass equal to 0.45359237 kg, while the pound-force (lbf) is a unit of force equal to 4.448 N. One pound of mass weighs one pound-force only under standard Earth gravity.
How do you find acceleration from force and mass?
Divide the net force by the mass: a = F ÷ m. A 200 N force on a 50 kg object produces an acceleration of 200 ÷ 50 = 4 m/s².