Use this calculator to compute Lumen values with step-by-step solutions.

How do I use this calculator?

Enter the required values; results and step-by-step derivation update automatically.

Photometry, engineering, research, and related scientific disciplines.

What formulas does this use?

All standard lumen formulas are applied and shown step-by-step in the results.

Can I get step-by-step solutions?

Yes. The calculator shows a full step-by-step derivation when results are displayed.

How accurate are the results?

Results use standard floating-point arithmetic (~15 significant digits). Suitable for education and professional use.

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Luminous Flux and Illuminance

Lumens (lm) measure total luminous flux; lux (lx) is illuminance (lumens per m²). Candela (cd) is luminous intensity. Efficacy (lm/W) links lumens to power. Inverse-square law: E = I/d² for point sources.

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1 lux = 1 lm/m²; 1 foot-candle ≈ 10.76 lux. Office task lighting: 300–500 lux; retail: 500–1000 lux. LED efficacy 80–150 lm/W vs incandescent ~15 lm/W. Inverse-square: doubling distance quarters illuminance.

Key quantities

Φ_v total luminous flux

Lumens

Key relation

E_v = Φ_v / A (illuminance)

Lux

Key relation

I_v = Φ_v / Ω (intensity)

Candela

Key relation

lm/W (lumens per watt)

Efficacy

Key relation

Ready to run the numbers?

Why: Photometry determines lighting design for offices, retail, outdoor, and residential. Efficacy drives LED adoption; lux levels define task requirements.

How: Lumens = total light output; lux = lumens/area. Point source: E = I/d². Room design uses utilization and maintenance factors. Efficacy: incandescent ~15, LED ~100+ lm/W.

1 lux = 1 lm/m²; 1 foot-candle ≈ 10.76 lux.Office task lighting: 300–500 lux; retail: 500–1000 lux.

Sources:CIE - Commission Internationale de l'ÉclairageNIST - Optical Radiation Physics

Run the calculator when you are ready.

Calculate LightingEnter lumens, lux, area, or efficacy for photometry

Input Parameters

Calculation Mode

Light Source Type

Lumens (lm)

Area

●Luminous Flux Results

LUMINOUS: DIMREADY

Lighting Results

Lumens

800 lm

Luminous flux

Lux

80.00 lx

7.43 fc

Candela

254.65 cd

Luminous intensity

Power

8.00 W

100 lm/W

Foot-candles

7.43 fc

Annual Cost

$3.50

Equiv. Incand.

53W

Equiv. CFL

13W

Equiv. LED

Fixtures (800lm)

Step-by-Step Calculation

Input Parameters

Lumens: 800 lm

Area: 10.00 m²

Lux Calculation

Formula: Lux = Lumens / Area

Lux = 800 / 10.00 = 80.00 lx→ 80.00 lx

Derived Values

Foot-candles: 7.43 fc

Candela: 254.65 cd

Power: 8.00 W (at 100 lm/W)

Annual Cost: $3.50 (at $0.12/kWh)

Visualizations

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

💡

A 100 W incandescent (~1500 lm) is replaced by ~15 W LED for same output.

— Energy Star

📐

Sunlight: ~100,000 lux; overcast: ~1,000 lux; office: 300–500 lux.

— Lighting handbooks

🔆

Candela defines luminous intensity in a given direction; 1 cd ≈ 1 candle.

— SI definitions

⚡

LED efficacy has improved from ~20 to 150+ lm/W over two decades.

— DOE lighting reports

📋 Key Takeaways

• Lumens measure total light output: The lumen (lm) quantifies the total amount of visible light emitted by a source, making it the standard unit for comparing bulb brightness regardless of technology
• Lux measures light on surfaces: Illuminance (lux) tells you how much light falls on a surface — 1 lux = 1 lumen per square meter. This is what matters for task lighting and room design
• Luminous efficacy determines efficiency: Measured in lumens per watt (lm/W), efficacy shows energy efficiency. LED bulbs achieve 100-150 lm/W vs 15 lm/W for incandescent, saving 85-90% energy
• Inverse square law applies to point sources: Light intensity decreases with distance squared — doubling distance reduces illuminance to 1/4. Critical for spotlight and fixture placement calculations

💡 Did You Know?

🌞The theoretical maximum luminous efficacy is 683 lm/W at 555nm (peak human eye sensitivity). Modern LEDs achieve up to 150 lm/W, approaching 22% of the theoretical limit.Source: CIE Photopic Luminous Efficiency Function

💡An 800-lumen LED bulb replaces a 60W incandescent while using only 8-10W — saving 50W per bulb. If every US household replaced one bulb, it would save enough energy to power 3 million homes.Source: Energy Star

📐The human eye is most sensitive to 555nm (green-yellow) light. This is why green laser pointers appear brighter than red or blue at the same power, and why efficacy peaks at this wavelength.Source: CIE Standard Observer

🏢Office lighting typically requires 300-500 lux. A 10m × 10m office needs about 30,000-50,000 lumens total. With 100 lm/W LEDs, that's 300-500W vs 2,000-3,300W with incandescent bulbs.Source: IES Lighting Handbook

🌙Full moonlight provides about 0.25 lux, while direct sunlight provides 100,000 lux. Indoor lighting ranges from 100-500 lux (residential) to 500-1,000 lux (offices and retail).Source: NIST Illuminance Standards

⚡LED technology has improved dramatically — efficacy increased from 30 lm/W in 2005 to 150+ lm/W today. The first LED bulb cost $50 in 2010; today equivalent bulbs cost under $5.Source: DOE LED Progress Report

🔬 How It Works

Photometry measures visible light as perceived by the human eye, using the CIE photopic luminous efficiency function that peaks at 555nm. Luminous flux (lumens) quantifies total light output, while illuminance (lux) measures light falling on surfaces. Luminous intensity (candela) describes directional brightness.

Luminous Flux

Φ = ∫ I(λ) V(λ) dλ

Total visible light output weighted by human eye sensitivity V(λ). Measured in lumens (lm).

Luminous Efficacy

η = Φ / P (lm/W)

Energy efficiency — lumens per watt. Maximum theoretical: 683 lm/W at 555nm.

Candela Relationship

I = dΦ / dΩ

Luminous intensity is flux per unit solid angle. For uniform sources: cd = lm / (4π sr).

Inverse Square Law

E = I / d²

Illuminance decreases with distance squared for point sources. Critical for fixture placement.

🎯 Expert Tips

📐

Use the lumen method for room design — calculate total lumens needed = (required lux × room area) / (utilization factor × maintenance factor). UF accounts for fixture efficiency and room reflectance; MF accounts for light loss over time.

🎨

Consider color temperature (CCT) for task lighting — warm white (2700-3000K) for residential, cool white (4000-5000K) for offices. Higher CCT can appear brighter at the same lumen output due to increased blue content.

🔦

Account for beam angle in directional lighting — narrow beams (15-30°) concentrate light for task lighting, while wide beams (120°+) provide general illumination. Candela values help calculate illuminance at specific distances.

⚙️

Factor in maintenance and utilization factors — typical UF = 0.5-0.7 for offices, MF = 0.7-0.9 depending on cleaning frequency. These reduce required initial lumens by 30-50%, saving energy and cost.

📊 Light Source Efficacy Comparison

Light Source	Typical Efficacy (lm/W)	Lifetime (hours)	800 lm Equivalent	Annual Cost*
Incandescent	15 lm/W	1,000 hrs	53W	$38.40
Halogen	20 lm/W	2,000 hrs	40W	$29.20
CFL	60 lm/W	10,000 hrs	13W	$9.50
LED Standard	100 lm/W	25,000 hrs	8W	$7.00
LED Premium	150 lm/W	50,000 hrs	5W	$4.38

*Based on 3 hours/day usage at $0.12/kWh

❓ Frequently Asked Questions

What is the difference between lumens and lux?

Lumens measure total light output from a source (luminous flux), while lux measures light falling on a surface (illuminance). Think of lumens as the "amount of light" and lux as "how bright a surface appears." For example, an 800-lumen bulb produces 800 lumens total, but the lux on your desk depends on distance and beam angle.

How many lumens do I need for a room?

It depends on room size and purpose. Use the formula: Total Lumens = (Required Lux × Room Area in m²) / (Utilization Factor × Maintenance Factor). For a 20 m² living room at 200 lux with UF=0.6 and MF=0.8: (200 × 20) / (0.6 × 0.8) = 8,333 lumens total. Divide by fixture lumens to get number of fixtures needed.

What is luminous efficacy and why does it matter?

Luminous efficacy (lm/W) measures how efficiently a light source converts electrical power into visible light. Higher efficacy means more light per watt, reducing energy costs. LED bulbs achieve 100-150 lm/W vs 15 lm/W for incandescent — a 10W LED produces the same light as a 60W incandescent, saving 83% energy.

How does distance affect light intensity?

Light follows the inverse square law: illuminance decreases with the square of distance. If you double the distance, illuminance drops to 1/4. For example, a 1000 cd spotlight produces 1000 lux at 1m, 250 lux at 2m, and 111 lux at 3m. This is critical for fixture placement in task lighting.

What is candela and how is it related to lumens?

Candela (cd) measures luminous intensity in a specific direction. For uniform point sources: cd = lm / (4π sr). For directional sources with beam angle θ: cd = lm / Ω, where Ω is the solid angle. A 1000-lumen bulb with 120° beam angle has ~63 cd, while the same lumens in a 15° beam has ~4,000 cd.

Can I use lumens to compare different light bulb types?

Yes! Lumens are the standard for comparing brightness across all bulb types. An 800-lumen LED, CFL, and incandescent produce the same amount of visible light, but use different power: 8W (LED), 13W (CFL), and 53W (incandescent). Always compare lumens, not watts, when choosing bulbs.

What are foot-candles and how do they relate to lux?

Foot-candles (fc) are the US customary unit for illuminance, while lux (lx) is the SI unit. 1 foot-candle = 10.764 lux. For example, 500 lux = 46.5 foot-candles. Most modern standards use lux, but older US lighting codes may reference foot-candles.

How do I calculate lighting for a specific task?

Use recommended lux levels: reading (300-500 lux), office work (300-500 lux), detailed work (500-750 lux), warehouse (100-200 lux). Calculate required lumens = lux × area, then account for utilization and maintenance factors. For task lighting, also consider beam angle — narrow beams (15-30°) concentrate light where needed.

📊 Lumens and Lighting by the Numbers

683

lm/W Maximum Theoretical Efficacy

800

lm = 60W Incandescent Equivalent

150

lm/W Best Commercial LED Efficacy

555

nm Peak Human Eye Sensitivity

📚 Official Sources

CIE - Commission Internationale de l'Éclairage

NIST - Optical Radiation Physics

IES - Illuminating Engineering Society

Energy Star - Light Bulbs

DOE - Lighting Choices Save You Money

⚠️ Disclaimer

This calculator is for educational and design purposes. Always verify calculations and use appropriate safety margins. For critical applications involving lighting design, energy code compliance, or industrial lighting systems, consult a licensed lighting designer or electrical engineer. Actual light output may vary based on fixture design, operating temperature, dimming, and aging. Efficacy values are typical ranges — actual performance depends on specific products and operating conditions. Always follow local building codes and energy efficiency standards (e.g., ASHRAE 90.1, IECC, Title 24).

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Luminous Flux and Illuminance

Input Parameters

Lighting Results

Step-by-Step Calculation

Visualizations

🔬 Physics Facts

📋 Key Takeaways

💡 Did You Know?

🔬 How It Works

🎯 Expert Tips

📊 Light Source Efficacy Comparison

❓ Frequently Asked Questions

What is the difference between lumens and lux?

How many lumens do I need for a room?

What is luminous efficacy and why does it matter?

How does distance affect light intensity?

What is candela and how is it related to lumens?

Can I use lumens to compare different light bulb types?

What are foot-candles and how do they relate to lux?

How do I calculate lighting for a specific task?

📊 Lumens and Lighting by the Numbers

📚 Official Sources

⚠️ Disclaimer

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Luminous Flux and Illuminance

Input Parameters

Lighting Results

Step-by-Step Calculation

Visualizations

🔬 Physics Facts

📋 Key Takeaways

💡 Did You Know?

🔬 How It Works

🎯 Expert Tips

📊 Light Source Efficacy Comparison

❓ Frequently Asked Questions

What is the difference between lumens and lux?

How many lumens do I need for a room?

What is luminous efficacy and why does it matter?

How does distance affect light intensity?

What is candela and how is it related to lumens?

Can I use lumens to compare different light bulb types?

What are foot-candles and how do they relate to lux?

How do I calculate lighting for a specific task?

📊 Lumens and Lighting by the Numbers

📚 Official Sources

⚠️ Disclaimer

Related Physics Calculators

Related Calculators

Angular Resolution Calculator

Aperture Area Calculator

Binoculars Range Calculator

Blackbody Radiation Calculator

Bragg's Law Calculator

Brewster's Angle Calculator

We Value Your Privacy