Work & Power Calculator · W = F·d·cosθ and P = W/t

Work & Power Calculator

Calculate work done from force, displacement and angle then find the power from work over time

Quick preset

Inputs

Force (F)

Displacement (d)

Angle (θ)

Time taken (t) — for power

Power unit (display)

Work: W = F × d × cos(θ) — energy transferred by a force. Power: P = W ⁄ t — how fast that work is done. Doubling the time halves the power; doubling the force doubles both.

Quick examples

Work & Power Results

Work done

— J

— — —

Power

— W

— —

Work · Kilojoules

— kJ

Work · Foot-pounds

— ft-lbs

Work · Calories

— cal

Work · Watt-hours

— Wh

Power · Kilowatts

— kW

Power · Horsepower

— hp(l)

Power · BTU / hour

— BTU/h

Power · cal / second

— cal/s

Work scale — what this compares to

Energy range	Scale	Examples

Power scale — what this compares to

Power range	Scale	Examples

Reference — common work & energy amounts

Action / source	Work	Category	Notes

Reference — common power ratings

Device / source	Power	Category	Notes

Embed this calculator

Embed code

Live preview — identical to the main calculator EXACT MATCH

\n'; }function generateEmbedCode() { var toolHtml = buildToolHtml(); if (embedCodeTextarea) embedCodeTextarea.value = toolHtml; if (embedPreview) embedPreview.srcdoc = toolHtml; }window.toggleEmbedPanel = function () { if (!embedPanel) return; var isHidden = (embedPanel.style.display === 'none' || embedPanel.style.display === ''); if (isHidden) { generateEmbedCode(); embedPanel.style.display = 'block'; try { embedPanel.scrollIntoView({ behavior:'smooth', block:'start' }); } catch (e) {} } else { embedPanel.style.display = 'none'; } };window.closeEmbed = function () { if (embedPanel) embedPanel.style.display = 'none'; }; window.refreshEmbed = function () { generateEmbedCode(); };window.copyEmbedCode = function () { if (!embedCodeTextarea) return; generateEmbedCode(); embedCodeTextarea.select(); embedCodeTextarea.setSelectionRange(0, embedCodeTextarea.value.length); if (navigator.clipboard) { navigator.clipboard.writeText(embedCodeTextarea.value).then(function () { alert('Embed code copied!'); }) .catch(function () { try { document.execCommand('copy'); alert('Embed code copied!'); } catch (e) { alert('Press Ctrl+C to copy'); } }); } else { try { document.execCommand('copy'); alert('Embed code copied!'); } catch (e) { alert('Press Ctrl+C to copy'); } } };/* ─────────── init ─────────── */ function bindAll() { [forceInput, distInput, angleInput, timeInput].forEach(function (el) { if (el) { el.addEventListener('input', calculate); el.addEventListener('change', calculate); } }); [forceUnitSelect, distUnitSelect, timeUnitSelect, powerDisplaySelect].forEach(function (el) { if (el) el.addEventListener('change', calculate); }); if (presetSelect) presetSelect.addEventListener('change', onPresetChange); }function init() { populatePresets(); bindAll(); calculate(); if (embedPanel) embedPanel.style.display = 'none'; }if (document.readyState === 'loading') { document.addEventListener('DOMContentLoaded', init); } else { init(); } })();

Relevant Tools

Elastic Potential Energy Calculator

Kinetic Energy Calculator

Power to Weight Ratio Calculator

Potential Energy Calculator

Bullet Energy Calculator

Creator & Maintainer

Faiq Ur Rahman is a web designer, digital product developer, and founder of Toolraxy, a growing platform of web-based calculators and utility tools. He specializes in building structured, user-friendly tools focused on health, finance, productivity, and everyday problem-solving.

Rate this Tool

User Ratings:

0 out of 5 stars (based on 0 reviews)

Excellent

Very good

Average

Poor

Terrible

Work & Power Calculator: Force, Displacement, and Time

Two physics calculations share one screen. Enter force, displacement, and angle, and the tool returns work in joules, kilojoules, foot-pounds, calories, and watt-hours. Add a time value, and it returns power in watts, kilowatts, horsepower, BTU per hour, and calories per second. Pick a preset like climbing stairs or a crane lift, or enter custom values. Results update as you type, and all math runs in your browser.

Work tells you how much energy a force transfers. Power tells you how fast that transfer happens. They’re related but distinct. A small motor and a large motor can do the same amount of work if you give the small one enough time. This calculator shows both numbers side by side, which makes the distinction concrete. It handles five force units, seven distance units, four time units, and six power display options. The dual-verdict banners label each result, so you can see at a glance whether your work is “High” and your power is “Moderate.” Eight presets cover common scenarios from lifting an apple to a crane lift.

How to Use This Work & Power Calculator

Pick a preset from the dropdown, or leave it on Custom / manual input.
Enter the force. Choose N, kN, lbf, kgf, or dyn.
Type the displacement. Units include m, cm, mm, km, ft, in, and mi.
Set the angle between force and motion in degrees. Use 0° for a push along the motion.
Add a time value. Units are seconds, minutes, hours, or days.
Choose a power display unit if you want a specific output format.
Watch both hero numbers update as you type.
Read the eight tiles for work and power in alternate units.

How the Work and Power Formulas Work

Work equals force times displacement times the cosine of the angle between them. Power equals work divided by time.

Formula: W = F × d × cos(θ)

Formula: P = W ÷ t

W is work in joules. F is force in newtons. d is displacement in meters. θ is the angle between the force vector and the displacement vector. P is power in watts, and t is time in seconds.

The cosine term controls how much of the force does useful work. At 0°, cos(0) = 1, so the full force counts. At 90°, cos(90) = 0, so no work is done. At 180°, cos(180) = −1, so the work is negative and the object loses energy.

The calculator converts every force unit to newtons and every distance unit to meters before multiplying. Time converts to seconds for the power calculation. If force or distance is negative, the tool shows a warning. Zero is allowed and returns zero work. The angle can be any value from −360 to 360 degrees.

Power follows directly from work and time. Doubling the time halves the power for the same work. Doubling the force doubles both work and power. The two hero displays update together so you can see the relationship in real time.

Worked Example

Load the stairs preset. Force is 687 N. Displacement is 10 m. Angle is 0°. Time is 8 seconds.

Step 1: Convert the angle to radians. 0° × π ÷ 180 = 0 rad.

Step 2: Find the cosine. cos(0) = 1.

Step 3: Multiply force by displacement. 687 × 10 = 6,870.

Step 4: Multiply by the cosine. 6,870 × 1 = 6,870 J.

The work hero shows 6.87 kJ. Now for power.

Step 5: Convert time to seconds. 8 s = 8 s.

Step 6: Divide work by time. 6,870 ÷ 8 = 858.75 W.

The power hero shows 858.75 W, which is about 0.86 kW or 1.15 hp. The work verdict banner labels this “High” work. The power verdict banner labels it “Moderate” power. Climbing 10 meters of stairs in 8 seconds is a hard effort for a person. The work is moderate in absolute terms, but the power output is near the top of what a human can sustain for a short burst.

If the same person took 16 seconds instead of 8, the work would stay at 6,870 J but the power would drop to 429 W. Same energy, half the rate. That’s the distinction the dual display makes visible.

What Is Work in Physics?

Work is the energy transferred when a force moves an object through a distance. It equals force times displacement times the cosine of the angle between them. The unit is the joule. A force that doesn’t move anything does no work, no matter how hard it pushes.

The concept matters because it connects force to energy. Every change in an object’s kinetic or potential energy comes from work done on it. A car engine does work to accelerate. Gravity does negative work when you lift something. Friction does negative work when you slide a box.

What Is Power in Physics?

Power is the rate at which work is done. It equals work divided by time. The unit is the watt, which is one joule per second. A 100 W light bulb uses 100 joules every second. A 1,000 W microwave uses ten times that.

Power matters because it tells you how fast energy moves. Two cranes can lift the same beam to the same height, doing identical work. But the crane that does it in half the time delivers twice the power. That’s why power ratings appear on everything from light bulbs to car engines.

How Do You Calculate Work and Power Together?

Multiply force by displacement by the cosine of the angle to get work. Then divide work by time to get power. A 200 N push over 5 m at 0° does 1,000 J of work. If it takes 4 seconds, the power is 250 W.

The two calculations chain together naturally. Work depends only on force, distance, and angle. Power adds the time dimension. You can think of work as the total energy transferred and power as the speed of that transfer.

Why Does the Angle Matter in the Work Formula?

Only the component of force along the direction of motion does work. The cosine term extracts that component. At 0°, the full force counts. At 90°, none of it counts. At 180°, the force opposes motion and does negative work.

This is why pulling a sled with a rope at an angle feels harder than pulling it horizontally. You’re wasting some force lifting the sled instead of moving it forward. The same effort produces less useful work.

What Is a Joule of Work?

A joule is the work done when a force of one newton moves an object one meter in the direction of the force. Lifting a small apple about one meter does roughly one joule of work. A heartbeat does about one joule. A 100 W light bulb running for one second uses 100 joules.

The work scale table labels ranges from negligible (below 1 J) to gigantic (above 1 GJ). A book lift is low. A crane lift is very high. A lightning bolt is gigantic.

What Is a Watt of Power?

A watt is one joule per second. An LED indicator light draws about 0.05 W. A phone charger draws about 5 W. A microwave runs at about 1,000 W. A car engine at 150 hp produces about 112,000 W.

The power scale table labels ranges from negligible (below 1 W) to gigawatt-scale (above 1 GW). A TV is moderate. A kettle is high. A wind turbine is massive. A nuclear reactor is gigawatt-scale.

What Is the Difference Between Work and Power?

Work is energy transferred. Power is the rate of that transfer. They’re measured in different units (joules vs. watts) and answer different questions. Work tells you how much. Power tells you how fast.

A person can do the same work as a small motor given enough time. The motor just does it faster. That’s why power ratings matter for engines and motors, but work totals matter for energy bills and fuel consumption.

What Does Negative Work Mean?

Negative work happens when the force points opposite to the displacement. Friction does negative work on a sliding box. Gravity does negative work on a rising rocket. The object loses energy instead of gaining it.

In the calculator, angles above 90° produce negative work. The verdict banner labels this “Negative work” and shows how much energy the object loses. That’s useful for braking and drag problems.

Common Mistakes When Calculating Work and Power

Forgetting to convert units is the most common error. Grams with meters, or pounds with centimeters, will give an answer that’s off by a large factor. Using the wrong angle is another. The angle is between the force and the displacement, not between the force and the ground.

Also, don’t confuse work with power. Work is energy; power is energy per unit time. A small engine can do a lot of work if you give it enough time. And don’t assume work is always positive. Angles above 90° give negative work.

Real-World Example: Climbing Stairs vs. Crane Lift

Climbing 10 meters of stairs takes about 6,870 J of work for an average adult. Done in 8 seconds, that’s 859 W of power. A crane lifting a 500 kg beam 20 meters does about 98,100 J of work. Done in 30 seconds, that’s 3,270 W.

The crane does about 14 times more work than the person. But the crane’s power output is only about 4 times higher because it takes longer to complete the lift. If the crane finished in 5 seconds, its power would be 19,620 W, more than 20 times the person’s output.

Benefits of Using This Work & Power Calculator

Dual results in one view: Work and power appear side by side, so you can see how time changes the power without changing the work.
Eight unit combinations: Force, distance, time, and power display each have multiple options, which removes the conversion step from manual calculations.
Eleven presets: Common scenarios from a heartbeat to a car engine are preloaded, giving you a fast starting point.
Four reference tables: Work scale, power scale, work reference, and power reference give you context for any result.
Instant feedback: Results update as you type, so you can compare scenarios without pressing a button.
Runs locally: All math happens in your browser. No data leaves your device, which matters for proprietary engineering estimates.
Works on any device: The layout adapts to phones, tablets, and desktops, so you can use it in a classroom, a lab, or at a job site.