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Formula
F = m × a
- F
- net force on the object, in newtons (N)
- m
- mass of the object, in kilograms (kg)
- a
- acceleration of the object, in meters per second squared (m/s²)
Newton’s second law in one line
Force is what changes an object’s motion. Newton’s second law says exactly how much: the net force on an object equals its mass times its acceleration.
F = m × a
Rearranged, it gives the other two forms the force calculator uses: m = F ÷ a and a = F ÷ m. With mass in kilograms and acceleration in meters per second squared, force comes out in newtons. One newton is the force that speeds up one kilogram by one meter per second every second.
How to use the force calculator
- Pick what you want to find: Force, Mass or Acceleration.
- Enter the two known values with their units. Mass can be in grams, kilograms, metric tons, ounces, pounds or US tons. Acceleration can be in m/s², ft/s² or g. Force can be in newtons, kilonewtons, dynes, pounds-force or kilograms-force.
- Choose the unit for the answer. The other common units appear below it.
- When solving for force, the result also compares the acceleration with gravity, as a multiple of the object’s own weight.
How to calculate force by hand
A 1,200 kg car accelerates at 2.5 m/s². The net force is:
F = 1,200 kg × 2.5 m/s² = 3,000 N (3 kN)
To express that in pounds-force, divide by 4.44822: 3,000 ÷ 4.44822 ≈ 674.4 lbf.
Solving for mass or acceleration
- A net force of 90 N gives a cart an acceleration of 3 m/s². Its mass is 90 ÷ 3 = 30 kg.
- A 250 N net force on a 50 kg crate gives an acceleration of 250 ÷ 50 = 5 m/s².
Working in US units
Pounds and pounds-force are linked through standard gravity. One pound-force is the weight of a one-pound mass where g = 9.80665 m/s². This gives a neat shortcut: a force in lbf divided by a mass in lb gives the acceleration in g. A 600 lbf net force on a 3,000 lb vehicle produces 0.2 g, or about 1.96 m/s². Mixing lbf with ft/s² without that conversion is a classic source of errors that are off by a factor of 32.17.
Force needed to accelerate a 1,500 kg car
| Acceleration | In g | Net force | In pounds-force |
|---|---|---|---|
| 1 m/s² | 0.102 g | 1,500 N | 337.2 lbf |
| 2 m/s² | 0.204 g | 3,000 N | 674.4 lbf |
| 3 m/s² | 0.306 g | 4,500 N | 1,012 lbf |
| 5 m/s² | 0.51 g | 7,500 N | 1,686 lbf |
The force scales in a straight line with the acceleration. Twice the acceleration needs twice the net force. These are net forces, so the engine must also overcome rolling resistance and air drag, which grow with speed.
Real-life uses
Vehicles and transport
Engineers use F = ma to size motors, brakes and tow hitches. To find the acceleration from a change in speed first, use the acceleration calculator.
Lifting and rigging
A load being lifted needs a force equal to its weight plus m × a to speed it up. A hoist that starts a 500 kg load moving at 0.5 m/s² must pull 500 × (9.80665 + 0.5) ≈ 5,153 N.
Sports science
Force plates measure the force athletes push into the ground. Dividing by body mass gives the acceleration they produce at take-off.
Physics problems
Many problems chain formulas together. Find the acceleration with F = ma, then the speed with the velocity calculator (v = v₀ + at), then the energy with the kinetic energy calculator.
Common mistakes
- Using one force instead of the net force. Subtract friction, drag and any opposing forces first.
- Mixing mass and weight. Mass is in kilograms. Weight is a force, in newtons. A “70 kg person” has a weight of about 686 N.
- Treating pounds as pounds-force. 1 lb is a mass and 1 lbf is a force. They are linked by g, not equal by definition in every unit system.
- Unit mismatches. Grams with m/s² gives millinewtons, not newtons. Convert grams to kilograms first.
- Forgetting direction. F = ma is a vector equation. In two dimensions, resolve forces into components first.
Glossary
- Newton (N): SI unit of force, 1 kg·m/s².
- Pound-force (lbf): the weight of a 1 lb mass under standard gravity, 4.44822 N.
- Kilogram-force (kgf): the weight of 1 kg under standard gravity, 9.80665 N.
- Standard gravity (g₀): 9.80665 m/s² by definition, used for g-force and for weight-based units.
- Inertia: an object’s resistance to changes in motion, measured by its mass.
Worked examples
Pushing a loaded cart
An 85 kg loaded cart speeding up at 1.4 m/s². What net force is needed?
Inputs (Force): Mass = 85; Mass unit = Kilograms; Acceleration = 1.4; Acceleration unit = Meters per second squared; Show force in = Newtons (N)
F = m × a = 85 kg × 1.4 m/s² = 119 N
Answer: Accelerating 85 kg at 1.4 m/s² takes a net force of 119 N.
Force in pounds-force from US units
A 3,500 lb car accelerating at 0.3 g. Because 1 lbf is the weight of 1 lb in standard gravity, the answer is simply 3,500 × 0.3.
Inputs (Force): Mass = 3500; Mass unit = Pounds; Acceleration = 0.3; Acceleration unit = Standard gravity (g); Show force in = Pounds-force (lbf)
Convert to SI units: 3,500 lb = 1,587.57 kg; 0.3 g = 2.942 m/s² F = m × a = 1,587.57 kg × 2.942 m/s² = 4,670.63 N 4,670.63 N = 1,050 lbf
Answer: Accelerating 3,500 lb at 0.3 g takes a net force of 1,050 lbf.
Acceleration of a sprinter
A 65 kg sprinter pushes off the blocks with a net horizontal force of 520 N.
Inputs (Acceleration): Net force = 520; Net force unit = Newtons; Mass = 65; Mass unit = Kilograms; Show acceleration in = Meters per second squared (m/s²)
a = F ÷ m = 520 N ÷ 65 kg = 8 m/s²
Answer: A net force of 520 N on 65 kg produces an acceleration of 8 m/s².
Edge case: mass from a force in kilonewtons and an acceleration in g
A net force of 19.6133 kN produces an acceleration of exactly 2 g (19.6133 m/s²).
Inputs (Mass): Net force = 19.6133; Net force unit = Kilonewtons; Acceleration = 2; Acceleration unit = Standard gravity (g); Show mass in = Kilograms (kg)
Convert to SI units: 19.6133 kN = 19,613.3 N; 2 g = 19.6133 m/s² m = F ÷ a = 19,613.3 N ÷ 19.6133 m/s² = 1,000 kg
Answer: A net force of 19.6133 kN accelerates a mass of 1,000 kg at 2 g.
Assumptions and limitations
- Uses Newton's second law for a constant mass, F = ma, where F is the net (resultant) force. If friction, drag or other forces act, enter the force left over after they are subtracted.
- Force, mass and acceleration are treated as magnitudes along one direction, so all inputs must be greater than zero.
- Units are converted to SI before calculating, using exact definitions from NIST. 1 lbf = 4.4482216152605 N, 1 kgf = 9.80665 N, 1 g = 9.80665 m/s², 1 lb = 0.45359237 kg.
- Not valid for objects whose mass changes as they move (such as rockets burning fuel), or at speeds near the speed of light.
- Results are shown to 6 significant figures.
Frequently asked questions
What is Newton's second law?
The net force on an object equals its mass times its acceleration, F = ma. A larger force produces a larger acceleration, and the same force accelerates a heavier object less.
How do I calculate force from mass and acceleration?
Multiply them. With mass in kilograms and acceleration in m/s², the answer is in newtons. A 1,200 kg car accelerating at 2.5 m/s² needs a net force of 1,200 × 2.5 = 3,000 N.
What is a newton?
One newton is the force that accelerates 1 kg at 1 m/s² (1 N = 1 kg·m/s²). It is roughly the weight of a small apple. 1 N is about 0.2248 pounds-force.
How do I convert newtons to pounds of force?
Divide by 4.4482216152605, or multiply by about 0.2248. 1,000 N is about 224.8 lbf. The calculator shows the result in N, kN, lbf and kgf at the same time.
How do I find mass from force and acceleration?
Divide the force by the acceleration, m = F ÷ a. If 90 N gives an acceleration of 3 m/s², the mass is 30 kg.
Is weight a force?
Yes. Weight is the gravitational force on a mass, W = m × g. With standard gravity, g = 9.80665 m/s², so a 70 kg person weighs about 686 N, or 154 lbf.
What is net force?
The vector sum of all forces acting on an object. If you push a box with 200 N and friction pushes back with 150 N, the net force is 50 N, and that is the value to use in F = ma.
Sources
- University Physics Volume 1, 5.3 Newton's Second Law — OpenStax (Rice University). Checked October 12, 2026.
- NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity — National Institute of Standards and Technology (NIST). Checked October 12, 2026.
- CODATA value: standard acceleration of gravity — NIST Physical Measurement Laboratory. Checked October 12, 2026.