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Force, Work and Power Calculator (F = m·a, W = F·d, P = W/t)

Force, mechanical work and power are three fundamental concepts in classical mechanics. Force F (newtons, N) is defined by Newton's Second Law: F = m × a, where m is mass (kg) and a is acceleration (m/s²). Work W (joules, J) is the energy transferred when a body moves under the action of a force: W = F × d, where d is displacement (m). Power P (watts, W) measures how quickly work is performed: P = W / t, where t is time (s). This calculator lets you find any of these quantities — force, mass, acceleration, work or power — from the remaining known values. Results are given in SI units, and additionally in kilojoules (kJ) or kilowatts (kW) where applicable.

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How the force, work and power calculator works

The calculator supports five calculation modes: • Calculate force: F = m × a — enter mass (kg) and acceleration (m/s²) to get force in newtons (N). • Calculate mass: m = F / a — enter force (N) and acceleration (m/s²) to get mass in kilograms (kg). • Calculate acceleration: a = F / m — enter force (N) and mass (kg) to get acceleration in m/s². • Calculate work: W = F × d — enter force (N) and distance (m) to get work in joules (J) and kilojoules (kJ). • Calculate power: P = W / t — enter work (J) and time (s) to get power in watts (W) and kilowatts (kW). Division by zero is guarded — if a denominator is 0, the result is returned as 0. All results are rounded to 4 significant figures.

Example: force needed to accelerate a car

A car with mass 1200 kg is to be accelerated at a = 3 m/s². We calculate the force: F = m × a = 1200 × 3 = 3600 N If the car travels 500 m under this force: W = F × d = 3600 × 500 = 1,800,000 J = 1800 kJ If this work is done in 60 s: P = W / t = 1,800,000 / 60 = 30,000 W = 30 kW

Frequently asked questions

What is force in physics?

Force is a physical quantity that causes a change in the state of motion or shape of a body. The SI unit of force is the newton (N). Newton's Second Law states F = m × a, where m is mass in kilograms and a is acceleration in m/s². A force of 1 N gives a body of mass 1 kg an acceleration of 1 m/s².

How do I calculate force from mass and acceleration?

Use the formula F = m × a. Example: a car of mass 1000 kg accelerating at 2 m/s² requires a force F = 1000 × 2 = 2000 N. Select the 'Calculate force' mode, enter the mass and acceleration, and the calculator returns the force in newtons.

What is mechanical work?

Mechanical work W (measured in joules, J) is the energy transferred when a body moves under the action of a force. The formula is W = F × d, where F is force (N) and d is the displacement in the direction of the force (m). Example: pushing a wardrobe with 200 N over 3 m does W = 200 × 3 = 600 J of work.

Use the formula W = F × d. Example: lifting a weight of 50 N through a height of 2 m gives W = 50 × 2 = 100 J. The calculator returns the result in joules (J) and kilojoules (kJ). Note: work is zero when the force is perpendicular to the direction of motion.

Power P (measured in watts, W) is the rate at which work is done or energy is converted. The formula is P = W / t, where W is work (J) and t is time (s). Example: doing 1000 J of work in 5 s corresponds to a power of P = 1000 / 5 = 200 W.

Use the formula P = W / t. Example: an electric motor does 30,000 J of work in 60 s — its power is P = 30,000 / 60 = 500 W = 0.5 kW. The calculator automatically converts the result from watts to kilowatts.

1 kJ = 1000 J. Joules are used for smaller energies (e.g. school physics experiments), while kilojoules are used for larger ones (e.g. food energy: 1 kcal ≈ 4.184 kJ). The calculator automatically shows work in both units.

Gravitational acceleration g ≈ 9.81 m/s² is the acceleration at which objects fall freely near the Earth's surface (without air resistance). It follows from the Earth's mass and Newton's law of universal gravitation. The weight force acting on a body of mass m is F = m × g.

From F = m × a we get m = F / a. Example: if an engine generates a force of 500 N and gives an acceleration of 2 m/s², the mass of the object is m = 500 / 2 = 250 kg. Select the 'Calculate mass' mode in the calculator.

Choose a calculation mode from the dropdown list: Calculate force (F = m × a), Calculate mass (m = F / a), Calculate acceleration (a = F / m), Calculate work (W = F × d) or Calculate power (P = W / t). Enter the required values and press Calculate. The calculator returns the result in SI units and, depending on the mode, also in kilojoules or kilowatts.

The calculator is for educational and informational purposes. Results are computed using F = m × a, W = F × d and P = W / t. Calculations assume rectilinear motion and a constant force acting in the direction of motion. In real engineering tasks account for friction, air resistance and other external factors.