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Force Calculator: Calculate Force, Mass, or Acceleration

Compute force from mass and acceleration using Newton's second law

PhysicsBy Numora physics teamReviewed by Numora science teamUpdated 

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Assumptions
kg
m/s²
N
Result
٩٨٫١

Net force in newtons

F = ma gives ٩٨٫١ when solving for Force (F).

In imperial units٢٢٫٠٥٣٨
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⚡ The answer

A force calculator applies Newton's second law F = ma to solve for any one of the three variables. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in meters per second squared (m/s²). One newton is the force required to accelerate one kilogram at one meter per second squared.

Quick takeaway

This Force Calculator applies Newton's second law, F = ma, allowing you to quickly determine force, mass, or acceleration. Whether you need to find the force exerted on an object, its mass given force and acceleration, or the acceleration resulting from a known force and mass, this tool provides instant calculations. It supports standard SI units (newtons, kilograms, meters per second squared) and offers convenient imperial unit conversions for broader context. Ideal for students, engineers, and anyone needing to understand the fundamental principles of classical mechanics, this calculator simplifies complex physics problems into straightforward inputs and clear results.

What is a force?

Use this force calculator to apply Newton's second law F = ma — solving for force given mass and acceleration, or rearranged to solve for mass or acceleration given the other two. This tool provides a direct application of one of the most fundamental principles in classical mechanics. Enter values in standard SI units (kilograms, meters per second squared, newtons) and the calculator instantly returns the result, complete with an imperial-unit conversion for broader context. It's built against the rigorous Système International unit definitions and references from OpenStax University Physics, ensuring accuracy and educational value for students and professionals alike.

The formula

F = m × a
  • F — force in newtons (N)
  • m — mass in kilograms (kg)
  • a — acceleration in meters per second squared (m/s²)

Source: Newton's second law of motion (Newton, Principia, 1687).

Worked examples

1Weight of a 10 kg object on Earth

Inputs
solveFor: forcemass: 10accel: 9.81force: 100
Walkthrough

F = m × a = 10 kg × 9.81 m/s² = 98.1 N. This is the weight of a 10 kg mass at Earth's surface — the force gravity exerts on it. In imperial units, that's about 22 pounds-force.

2Car accelerating at 3 m/s²

Inputs
solveFor: forcemass: 1500accel: 3force: 100
Walkthrough

F = 1,500 kg × 3 m/s² = 4,500 N. That's the net force the engine must produce to accelerate a 1,500 kg car at 3 m/s² — about 1,012 pounds-force. Real-world drag and tire rolling resistance increase the required engine force above this 'ideal' value.

3Solve for acceleration: 100 N pushing 50 kg

Inputs
solveFor: accelmass: 50accel: 9.81force: 100
Walkthrough

a = F / m = 100 N / 50 kg = 2 m/s². A 100 N force on a 50 kg object produces 2 m/s² of acceleration. Half the mass would double the acceleration to 4 m/s²; double the mass would halve it to 1 m/s².

How to use this calculator

  1. Solve for (default: force)
  2. Mass — Mass of the object in kilograms. 1 kg = 2.205 lbs.
  3. Acceleration — Acceleration in meters per second squared. Earth's gravity is 9.81 m/s².
  4. Force — Force in newtons. 1 N = the force needed to accelerate 1 kg at 1 m/s².
  5. Read the result. Use the worked examples below to sanity-check against a known scenario.

Force units across common systems

SystemUnitDefinition
SInewton (N)kg · m/s²
CGSdyneg · cm/s² = 10⁻⁵ N
Imperialpound-force (lbf)≈ 4.4482 N
Engineeringkilogram-force (kgf)= 9.80665 N
Atomicatomic unit of force≈ 8.2387 × 10⁻⁸ N

SI is the standard for physics; pound-force still common in US engineering.

Frequently asked questions

What is Newton's second law?
The force on an object equals its mass times its acceleration: F = ma. Stated in Newton's Principia (1687), it's one of the three laws of motion that founded classical mechanics.
What's the difference between mass and weight?
Mass is how much matter is in an object (kg). Weight is the force gravity exerts on that mass (N). On Earth: weight = mass × 9.81. The same mass weighs less on the Moon (gravity ≈ 1.62 m/s²) but has the same mass.
What is one newton in everyday terms?
About the force needed to lift a small apple — roughly 102 grams of mass at Earth's gravity. 1 N = 0.225 pounds-force.
How do I convert pounds to newtons?
Multiply pounds-force by 4.4482 to get newtons. So a 200 lbf load is about 890 N. To go the other way, divide newtons by 4.4482.
Does F = ma work for objects in free fall?
Yes. The force is gravity (F = m × g where g ≈ 9.81 m/s²), and the resulting acceleration is g — meaning all objects fall at the same rate in vacuum, regardless of mass.
What if there's friction?
Use the net force in F = ma. Net force = applied force − friction force. So if you push a box with 100 N and friction is 30 N, the net force is 70 N and the acceleration is (70 N) / mass.
Can I use F = ma for multiple forces?
Yes, but use the vector sum of all forces. For 1D problems, add forces with sign (positive in the direction of motion). For 2D/3D, break forces into components and apply F = ma along each axis separately.
Does F = ma work at high speeds?
It's a Newtonian approximation valid at speeds far below the speed of light. At relativistic speeds, you need F = dp/dt where p is relativistic momentum (γmv). For everyday physics — cars, sports, engineering — F = ma is exact for practical purposes.

Force glossary

Force
Any interaction that, when unopposed, changes the motion of an object. Measured in newtons (N) in SI units.
Mass
A measure of an object's resistance to acceleration. Measured in kilograms (kg). Distinct from weight, which is the force gravity exerts on a mass.
Acceleration
Rate of change of velocity over time. Measured in m/s². Earth's gravitational acceleration at the surface is 9.81 m/s².
Newton (N)
SI unit of force. One newton is the force required to accelerate 1 kg at 1 m/s².
Pound-force (lbf)
Imperial unit of force. The force gravity exerts on 1 pound of mass at Earth's surface. 1 lbf ≈ 4.4482 N.
Inertial frame
A reference frame in which Newton's laws hold — one that is not accelerating. F = ma applies only in inertial frames.

How we built this calculator

Methodology

Newton's second law of motion states that the force on an object equals its mass times its acceleration: F = ma. The relationship is linear and applies in any inertial reference frame.

This calculator was written by Numora physics team and reviewed by Numora science team before publication. Both names link to full bios with verifiable credentials.

Formula source
Newton's second law of motion (Newton, Principia, 1687)
Last reviewed
2026-04-29
Reviewer
Numora science team
Calculation runs
Client-side only
NP
WRITTEN BY
Numora physics team
NS
REVIEWED AND APPROVED BY
Numora science team
In this review:
  • Verified the formula matches Newton's second law of motion (Newton, Principia, 1687) (Standard Système International (SI) units).
  • Confirmed the rounding rule applied by the engine: results to 4 decimal places.
  • Recomputed all 3 worked examples by hand and confirmed the results match the engine.
  • Confirmed all 5 cited sources resolve to current pages on the issuing institution.
  • Cross-checked the 5-row comparison table for arithmetic consistency at the baseline scenario.

Reviewed on 2026-04-29 · Next review: 2027-04-29

See editorial policy

Sources & references

Every numeric assumption traces to a primary source.

  1. Newton, Philosophiæ Naturalis Principia Mathematica (1687)INT
  2. NIST Reference on Constants, Units, and UncertaintyUSA
  3. OpenStax University Physics, Volume 1 — Chapter 5INT
  4. MIT OpenCourseWare 8.01 — Classical MechanicsUSA
  5. BIPM SI Brochure (2019)INT
  6. Numora Editorial Policy. numora.net/editorial-policy