Air Conditioning - HVAC - Cooling load conversion calculations

Convert between kW/ton, COP, and EER with our guide. Includes a formula table, step-by-step calculation methods, and practical examples for HVAC pros.

Follow us on Twitter 
Question, remark ? Contact us at contact@myengineeringtools.com

1. Introduction to Cooling Load Conversions

What are the basic units and metrics for HVAC cooling load conversions?

In the HVAC field, cooling load conversions are a cornerstone for accurate system design, energy efficiency, and performance comparisons. These conversions involve translating cooling loads between units such as tons of refrigeration (TR), kilowatts (kW), and British Thermal Units per hour (Btu/h), as well as efficiency metrics like Coefficient of Performance (COP), Energy Efficiency Ratio (EER), and kilowatts per ton (kW/ton). Understanding these conversions is essential for engineers and technicians working with commercial and industrial air-conditioning, heat pump, and refrigeration systems.

The primary units and efficiency metrics in cooling load calculations are:

• Tons of Refrigeration (TR): A traditional unit of cooling capacity, defined as the heat required to melt one ton (2000 lbs) of ice in 24 hours. Equivalent to 12,000 Btu/h or 3.517 kW.
• Kilowatts (kW): The standard SI unit for power, commonly used for larger systems.
• British Thermal Units per Hour (Btu/h): A traditional unit for heat removal, often used in residential and smaller commercial systems.
• Coefficient of Performance (COP): A dimensionless ratio of useful cooling output to power input. Higher COP indicates greater efficiency: \[ \text{COP} = \frac{\text{Useful Cooling Output (kW or Btu/h)}}{\text{Power Input (kW or Btu/h)}} \]
• Energy Efficiency Ratio (EER): A metric for unitary systems, calculated as net cooling capacity (Btu/h) divided by electrical power input (W). Higher EER indicates greater efficiency: \[ \text{EER} = \frac{\text{Net Cooling Capacity (Btu/h)}}{\text{Electrical Power Input (W)}} \]
• Kilowatts per Ton (kW/ton): A metric for larger systems, relating electrical power consumption (kW) to cooling capacity (TR). Lower kW/ton indicates higher efficiency: \[ \text{kW/ton} = \frac{\text{Electrical Power Consumption (kW)}}{\text{Cooling Capacity (TR)}} \]

Conversions between these units rely on established relationships. For example, converting 10 TR to kW:
10 TR × 3.517 kW/TR = 35.17 kW.

Efficiency metrics can also be interconverted. A common example is the relationship between COP and kW/ton:\[ \text{COP} = \frac{3.517}{\text{kW/ton}}\] For practical purposes, this is approximated as `COP = 3.52 / kW/ton`. For a system with a COP of 4.0, the kW/ton rating is:
kW/ton = 3.52 / 4.0 = 0.88 kW/ton.

These conversions are vital for comparing system efficiencies, sizing equipment, and ensuring compliance with industry standards. Lower kW/ton or higher COP and EER values indicate more efficient systems.

2. Importance of Converting Between kW/ton, COP, and EER

Why is it important to convert between kW/ton, COP, and EER?

Converting between kW/ton, Coefficient of Performance (COP), and Energy Efficiency Ratio (EER) is critical for accurately comparing HVAC and refrigeration system efficiencies across applications and standards. These metrics serve distinct purposes and are used in various contexts, making their interrelationships essential for informed decision-making in system design, procurement, and performance evaluation.

• Standardization and Comparability: Different regions and industries prefer specific metrics. For example, COP is common in commercial chillers, EER in residential air conditioning, and kW/ton in large-scale industrial systems. Converting between these metrics allows for standardized comparisons, ensuring systems are evaluated on a common basis.
• Compliance with Industry Standards: Regulatory bodies often specify efficiency requirements in one or more of these metrics. Converting between them ensures compliance with standards and facilitates certification processes.
• System Design and Sizing: Engineers rely on these metrics to size equipment appropriately. Lower kW/ton values indicate higher efficiency, reducing energy consumption and operating costs. Converting between metrics aids in selecting the most efficient system for a given cooling load.
• Energy Efficiency Analysis: Understanding the relationships between kW/ton, COP, and EER enables comprehensive efficiency analysis. Key formulas include:
  • COP = 3.52 / kW/ton
  • EER = 12 / kW/ton
  • COP = EER / 3.412
• Cost-Benefit Analysis: Conversions help evaluate the economic benefits of different systems. Systems with higher COP or EER and lower kW/ton generally have lower operating costs, making them more cost-effective despite higher initial investments.
• Global Applicability: Different regions use different metrics (e.g., EER in the U.S. and COP in Europe). Converting between them ensures global comparability, fostering international trade and collaboration.
• Technological Advancements: As new technologies emerge, their efficiency must be quantified using established metrics. Converting between kW/ton, COP, and EER allows for integration into existing frameworks, driving industry progress.
• Environmental Impact: Higher efficiency metrics reduce energy consumption and greenhouse gas emissions, contributing to sustainability goals. Conversions help identify and promote environmentally friendly technologies.

3. Key Formulas and Calculation Methods

What are the key formulas for converting HVAC efficiency metrics?

Converting between cooling load metrics is essential for accurate system design and performance comparison. The table below summarizes the key formulas, using precise constants for TR-kW conversions and standard industry approximations for efficiency metrics.

3.1. Step-by-Step Conversion from kW/ton to COP

Step 1: Understand the Relationship
The relationship between kW/ton and COP is:\[ \text{COP} = \frac{3.52}{\text{kW/ton}}\] Lower kW/ton values indicate higher efficiency, corresponding to higher COP.

Step 2: Apply the Formula
For a system with a kW/ton rating of 0.88:\[ \text{COP} = \frac{3.52}{0.88} = 4.0\] The system has a COP of 4.0, producing 4 units of cooling per unit of energy input.

3.2. Step-by-Step Conversion from kW/ton to EER

Step 1: Understand the Relationship
The relationship between kW/ton and EER is:\[ \text{EER} = \frac{12}{\text{kW/ton}}\] Lower kW/ton values correspond to higher EER, indicating greater efficiency.

Step 2: Apply the Formula
For a system with a kW/ton rating of 0.88:\[ \text{EER} = \frac{12}{0.88} \approx 13.64\] The system has an EER of approximately 13.64.

3.3. Step-by-Step Conversion from COP to EER

Step 1: Understand the Relationship
The relationship between COP and EER is:\[ \text{EER} = \text{COP} \times 3.412\] The constant 3.412 is the conversion factor between Btu/h and Watts.

Step 2: Apply the Formula
For a system with a COP of 4.0:\[ \text{EER} = 4.0 \times 3.412 \approx 13.65\] The system has an EER of approximately 13.65.

3.4. Step-by-Step Conversion from EER to COP

Step 1: Understand the Relationship
The relationship between EER and COP is:\[ \text{COP} = \frac{\text{EER}}{3.412}\]

Step 2: Apply the Formula
For a system with an EER of 13.8:\[ \text{COP} = \frac{13.8}{3.412} \approx 4.0\] The system has a COP of approximately 4.0.

4. Calculation Examples

Can you provide examples of cooling load conversion calculations?

Here are practical examples illustrating cooling load conversions in HVAC system design and analysis.

4.1. Converting TR to kW and Btu/h

Example 1:
A cooling system has a capacity of 15 TR. Convert this to kW and Btu/h.

Solution:

• TR to kW: \[ 15 \, \text{TR} \times 3.517 \, \text{kW/TR} = 52.755 \, \text{kW} \]
• TR to Btu/h: \[ 15 \, \text{TR} \times 12,000 \, \text{Btu/h/TR} = 180,000 \, \text{Btu/h} \]

Example 2:
A chiller provides 200,000 Btu/h of cooling. Convert this to TR and kW.

Solution:

• Btu/h to TR: \[ \frac{200,000 \, \text{Btu/h}}{12,000 \, \text{Btu/h/TR}} \approx 16.67 \, \text{TR} \]
• Btu/h to kW: \[ \frac{200,000 \, \text{Btu/h}}{3412 \, \text{Btu/h/kW}} \approx 58.62 \, \text{kW} \]

4.2. Converting Between COP, EER, and kW/ton

Example 3:
A chiller has a COP of 4.5. Convert this to kW/ton and EER.

Solution:

• COP to kW/ton: \[ \text{kW/ton} = \frac{3.52}{4.5} \approx 0.782 \, \text{kW/ton} \]
• COP to EER: \[ \text{EER} = 4.5 \times 3.412 \approx 15.35 \]

Example 4:
A system has an EER of 13.5. Convert this to COP and kW/ton.

Solution:

• EER to COP: \[ \text{COP} = \frac{13.5}{3.412} \approx 3.96 \]
• EER to kW/ton: \[ \text{kW/ton} = \frac{12}{13.5} \approx 0.889 \, \text{kW/ton} \]

4.3. Practical Application in System Design

Example 5:
Design a cooling system for a commercial building requiring 500 kW of cooling capacity. Determine the equivalent capacity in TR and Btu/h.

Solution:

• kW to TR: \[ \text{TR} = \frac{500 \, \text{kW}}{3.517 \, \text{kW/TR}} \approx 142.16 \, \text{TR} \]
• kW to Btu/h: \[ 500 \, \text{kW} \times 3412 \, \text{Btu/h/kW} = 1,706,000 \, \text{Btu/h} \]

Example 6:
A chiller has a cooling capacity of 100 TR and consumes 30 kW of power. Calculate its COP, EER, and kW/ton.

Solution:

• Calculate kW/ton: \[ \text{kW/ton} = \frac{30 \, \text{kW}}{100 \, \text{TR}} = 0.3 \, \text{kW/ton} \]
• Calculate COP from kW/ton: \[ \text{COP} = \frac{3.52}{0.3} \approx 11.73 \]
• Calculate EER from kW/ton: \[ \text{EER} = \frac{12}{0.3} = 40 \]

These examples demonstrate the practical application of cooling load conversions in HVAC system design, energy efficiency analysis, and performance comparisons.

5. Air conditioning cooling loads conversion online calculator

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

5.1 Excel (click here to show / hide the calculator)

You can download the calculator here : link

Sources

• https://www.engineeringtoolbox.com/cop-eer-d_409.html
• https://www.scribd.com/doc/199060208/Converting-Kw-Ton-to-COP-or-EER
• https://www.engineeringtoolbox.com/cooling-loads-d_665.html
• https://www.thermcoenergysystems.com/converting_kw_ton_cop_eer.html
• https://www.adicotengineering.com/eer-seer2-cop-hspf2-kwton-converter
• https://aircondlounge.com/cop-seer-eer-kw-ton-ceer-hvac-efficiency-guide/