How this instrument works
Newton's second law fixes what a force does: it accelerates mass. One newton acting alone on one kilogram produces one metre per second squared, and doubling either factor doubles what comes out. Newton himself never wrote F = ma — Principia (1687) says instead that change of motion is proportional to impressed force, a statement about momentum. Euler recast that sentence into today's algebraic shape around 1750, and every mechanics course since has taught Euler's version under Newton's name.
Everyday magnitudes are worth carrying in your head. A newton is small — roughly what a 102-gram apple presses onto your palm. An adult of 70 kg is held up by about 687 N of floor. Brakes hauling a family car down from motorway speed work in kilonewtons; Falcon 9's first stage leaves its pad on some 7.6 meganewtons. Since 2019 all three ingredients — kilogram, metre, second — rest on fixed constants of nature, so this unit inherits its size from physics rather than from any artefact in a vault.
Two conditions bound that multiplication. F means net force, everything pushing and pulling added as vectors: slide a crate across concrete at walking pace and your shove is real, yet friction cancels it, leaving zero acceleration and zero resultant. Your frame must also be inertial — measure from a braking bus or spinning platform and phantom terms appear. Where propellant is being thrown overboard, or speeds climb toward light, retreat to F = dp/dt; changing mass breaks any shortcut built on constant m.
- Enter the object's Mass — kilograms by default, with grams, tonnes and pounds on its unit menu.
- Enter Acceleration in m/s². Switch to ft/s² for imperial data, or to g0 to work in multiples of standard gravity.
- Read Force in newtons, or pick kN, lbf or kgf; four significant figures are carried.
- If several forces act at once, add them as vectors first and enter only what survives — this law wants a resultant, never one lone push.
Worked example — a newton, by definition
Set a one-litre bottle of water — 1.000 kg — on an air track, and push so that it gains exactly one metre per second of speed in every second. Enter Mass 1 kg, Acceleration 1 m/s², and Force reads 1 N. Not approximately: this pairing is how SI defines a newton, so an exact answer is guaranteed by construction, not by rounding luck.
One newton is a modest push. Hold a medium apple, near 102 grams, and your hand supplies almost precisely that: 0.102 × 9.80665 = 1.00 N. Which makes this calibration case a pleasant thing to remember — Newton's own fruit, sitting still in your palm, weighs one unit of a quantity later named for him. Raise Mass to 10 kg at that same 1 m/s² and Force climbs to 10 N; proportionality holds strictly in both factors.
Questions
Should I enter mass or weight?
Mass. That field wants kilograms, grams, tonnes or pounds-mass — a quantity unchanged by where you stand, Earth or Moon. If what you hold is a weight in newtons or pounds-force, divide by 9.80665 m/s² first to recover mass. Bathroom scales blur this distinction: they sense force and print kilograms, which is convenient here and wrong anywhere else.
Is F any single force, or all of them together?
All of them, summed as vectors — physicists call it net or resultant force. Push a filing cabinet at steady walking pace and you are certainly applying force, yet acceleration is zero, because friction matches your effort exactly and cancellation is total. Enter whatever survives that cancellation. A body under several large but balanced forces accelerates no more than an untouched one.
What are kgf and lbf on the unit menu?
Gravitational force units, still common in engineering tables. One kilogram-force is what standard gravity exerts on one kilogram: 9.80665 N, exactly. One pound-force is 4.4482216152605 N, also exact by definition. They persist in bolt-torque charts, lift capacities and hydraulic ratings. Choosing either on that output field only relabels results; arithmetic underneath always runs in newtons.
When does F = ma stop being true?
Three situations. Non-inertial frames: observe from an accelerating car or rotating platform and fictitious terms must be added by hand. Variable-mass systems: a rocket burning propellant needs F = dp/dt with an added thrust term, since m shrinks while speed grows. And motion approaching light speed, where relativistic momentum takes over. Below a few percent of light speed, in a frame not itself accelerating, with mass fixed, this product is exact past any precision you can measure.
How do I get an object's weight from this?
Set Acceleration to standard gravity, 9.80665 m/s² — or select g0 on that field and enter 1. A 70 kg adult then reads 686.5 N, that person's weight on Earth. Swap in 1.625 m/s² for lunar gravity and identical 70 kg now weighs 113.8 N, while Mass never moves. Weight is a force and varies with location; mass does not.
How does force relate to momentum and impulse?
Force is a rate of change of momentum, which was Newton's own phrasing. Multiply force by however long it acts and you get impulse, equal to momentum gained or lost. This explains crumple zones and airbags: a crash must remove some fixed amount of momentum, but stretching that removal over more milliseconds cuts peak force proportionally. Same change, gentler treatment.