Hydronic Balancing DIY – Step 4: Calculate Radiator Output

by Martin Schlobach | Last updated: Feb 3, 2024 | 0 comments

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In the fourth step of the “Hydronic Balancing DIY” series, we will focus on how to calculate radiator output for existing radiators. We need the radiator output to determine whether the installed radiators are sufficiently dimensioned for the desired system temperatures. Furthermore, in the next step, we can use the calculated radiator outputs and the calculated room loads to determine the necessary volume flows and presettings for the respective radiators.

Table of Contents

1 Determining the radiator output
2 Overview of all Calculated Radiator Outputs
3 Conclusion

Determining the radiator output

In the following section, I will first show you how to determine the radiator output manually. Later in this article, I will use an example to introduce the online radiator calculator from the German Heat Pump Association. This tool allows you to easily calculate radiator output for various types such as panel radiators, cast iron radiators, tubular steel radiators, and steel radiators online.

Directly to the example: Online Radiator Calculator

How to Calculate Radiator Output Manually

If you know the radiator output of your radiators (e.g. from product catalogues or manufacturer documentation), you can skip the individual steps in this section. All you need to do is convert the known output data to your desired system temperature using the following conversion factor for the “standard radiator output”.

As there is no data or product information on the existing radiators in our example building, we will calculate the radiator output of the individual radiators. Before we can calculate the radiator output, it is necessary to determine the conversion factor for the so-called standard radiator output.

Determine Conversion Factor for Standard Radiator Output

In the radiator standard DIN EN 442, the standard radiator output (standard heat output), which is determined by recognised test centres for each radiator, is calculated using the system temperatures 75/65/20 (flow 75 °C, return 65 °C and room temperature 20 °C).

However, as we are aiming for a system temperature of 75/55/22 in our heating system (see step 3 of the series “Doing hydraulic balancing yourself”), we need to carry out a conversion to these temperatures. The conversion is carried out using the logarithmic excess temperature with standard temperatures and the logarithmic excess temperature with operating temperatures. To do this, we only need the system temperatures already mentioned and enter these into the following formula. The factors in the formula stand for

$\Delta \vartheta_{ln}$ – logarithmic excess temperature
$\vartheta_{V}$ – flow temperature
$\vartheta_{R}$ – Return flow temperature
$\vartheta_{L}$ – air temperature

$\boxed{\Delta \vartheta_{ln}={\frac{\vartheta_{V}-\vartheta_{R}}{\ln \frac{\vartheta_{V}-\vartheta_{L}}{\vartheta_{R}-\vartheta_{L}}}}}$

Using this formula, we can now calculate the logarithmic excess temperature of the “operating case” (75/55/22) and the “standard case” (76/65/20). Firstly, we calculate the logarithmic excess temperature for operating temperatures (75/55/22) and obtain 42.2 Kelvin:

$\boxed{\Delta \vartheta_{ln,operation}={\frac{75 ^{\circ}C-55 ^{\circ}C}{\ln \frac{75 ^{\circ}C-22 ^{\circ}C}{55 ^{\circ}C-22 ^{\circ}C}}}=42,2 K}$

Now we calculate the logarithmic excess temperature for standard temperatures (75/65/20) and obtain 49.8 Kelvin:

$\boxed{\Delta \vartheta_{ln,Norm}={\frac{75 ^{\circ}C-65 ^{\circ}C}{\ln \frac{75 ^{\circ}C-20 ^{\circ}C}{65 ^{\circ}C-20 ^{\circ}C}}}=49,8 K}$

With the excess temperatures determined for the operating case of 42.2 Kelvin and the standard case of 49.8 Kelvin, we can now calculate the factor (f) for determining the radiator output. This results from the following formula

$\boxed{f=\frac{\Delta \vartheta_{ln,Betrieb}}{\Delta \vartheta_{ln,Norm}}}}$

If we insert the determined excess temperatures into the formula, we obtain the factor f=0.847, which is used for the further calculations.

$\boxed{f=\frac{42.2 K}{49.8 K}=0.847}$

How to Calculate Radiator Output for Various Radiator Types

In our example building, panel radiators, a towel radiator and underfloor heating are installed. To calculate the radiator output during operation (also known as the operating heat output), we need the standard heat output of the radiators, our calculated conversion factor f and the radiator exponent n.

Standard heat output $\dot Q_{Norm}$ : Heat output of a radiator determined under standardised conditions and system temperatures 75/65/20. Obtained from data sheets or roughly calculated.

Conversion factor f: Determined conversion factor for calculating the operating heat output. In our example 0.847.

Radiator exponent n: The radiator exponent n describes how effectively a radiator emits heat, depending on its own temperature compared to the room temperature. A low value close to 1 means that the heat output is very efficient and predictable. Higher values mean that this relationship is less direct and therefore less efficient. The radiator exponents of the various radiators can be found in the report from DeltaQ – Heating surface types (Recknagel Sprenger) – The document is unfortunately only available in german.

Calculation of Panel Radiators

I will start with the calculation of the panel radiators and carry out an example calculation for radiator no. 1 in the anteroom. This is a profiled panel radiator with the following dimensions:

Radiator type: Valve radiator PKP 21
Depth: 80 mm
Height: 500 mm
Width: 800 mm
Pre-adjustable valve: Yes
Type: Danfoss

In the first step of the calculation, we go to the DeltaQ report – heating surface types (Recknagel Sprenger) and look for the table with the standard heat outputs for vertically profiled panel radiators. In our example, this can be found on page 3 – table 0-1 (see Figure 1).

As you will soon realise, there is no radiator with a depth of 80 mm in this table. I have therefore decided to use the value for type 21, which corresponds to 100 mm. Thus, with the values given, we arrive at a radiator output of 1,212 W/m and a radiator exponent of 1.3.

Figure 1: Example calculation for panel radiators, source of the table: DeltaQ - heating surface types (Recknagel Sprenger) — Figure 1: Example calculation for panel radiators, source of the table: DeltaQ – heating surface types (Recknagel Sprenger)

As the standard heat output refers to watts per metre [W/m], we must take the radiator width B [m] of 0.8 m into account in the calculation. The operating heat output is calculated using the following formula:

$\boxed{\dot Q_{operation}=\dot Q_{standard} \cdot f^n \cdot B}$

If we now enter the determined values, we obtain an operating heat output of 781.3 W

$\boxed{\dot Q_{operation}=1212W/m \cdot 0.847^{1.3} \cdot 0,8m=\underline{\underline{781,3W}}}$

If we now compare the determined room heating load of the anteroom (see step 2 of the series hydraulic balancing yourself) of 630 W with the radiator output of 781.3 W, it becomes clear. The operating heat output is sufficient for the desired system temperatures of 75/55/22, indicating that the calculated radiator output meets the heating requirements.

Below I have calculated all the panel radiators for our example house and entered them in Table 1. During the calculation of the panel radiators with the system temperatures 75/55/22, I quickly realised that approx. 90 % of the radiators were far oversized. I therefore also calculated the radiator output at a system temperature of 70/50/22 as a trial. Interestingly, the radiator output was also sufficient for approx. 80 % of the radiators. Table 1 shows all the outputs of the panel radiators for the two system temperatures (75/55/22 and 70/50/22).

Note: Radiator 3 is a smooth-walled panel radiator.

Room	HK no.	Room load	HK capacity (75/55/22)	HK capacity (70/50/22)
Anteroom (GF)	1	630 W	781 W	662 W
Toilet (GF)	2	90 W	391 W	331 W
Washroom (GF)	3	130 W	281 W	238 W
Living room (GF)	5	1830 W	1501 W	1271 W
	6		1501 W	1271 W
Corridor (GF)	7	380 W	433 W	366 W
Bedroom (UF)	8	550 W	1092 W	924 W
Office (UF)	10	990 W	819 W	693 W
Guest (UF)	11	670 W	1019 W	863 W

Table 1: Radiator output of the panel radiators at different

Calculation of the Towel Radiator

Now that we have determined the radiator outputs of the panel radiators, let’s continue with the calculation of the towel radiator in the bathroom on the upper floor. This is a towel radiator with the following dimensions:

Radiator type: Compact radiator
Height: 1900 mm
Width: 500 mm
Pre-adjustable valve: Yes
Type: Danfoss

Firstly, we go to the DeltaQ report – Heating surface types (Recknagel Sprenger) and look for the table with the standard heat outputs for towel radiators. This can be found in our example on page 8 – table 0-7 (see figure 3).

As the measured width does not correspond to the exact values in the table, I have selected the values that come closest to the measured values. I choose a radiator height of 1,852 mm and a width of 516 mm. This gives us a radiator output of 934 W and a radiator exponent of 1.26.

Figure 2: Example calculation for towel radiators, source of the table: DeltaQ - heating surface types (Recknagel Sprenger) — Figure 2: Example calculation for towel radiators, source of the table: DeltaQ – heating surface types (Recknagel Sprenger)

This results in the following formula:

$\boxed{\dot Q_{operation}=\dot Q_{standard} \cdot0,847^n}$

$\boxed{\dot Q_{operation}=934W \cdot 0.847^{1.26} =\underline{\underline{757.7W}}}$

We now compare the determined room heating load of the bathroom on the upper floor (see step 2 of the series hydraulic balancing yourself) of 410 W with the determined radiator output of 757.7 W. We can see that the radiator output is sufficient for the desired system temperatures of 75/55/22 and is even oversized.

The calculation with a system temperature of 70/50/22 resulted in a radiator output of 644.5 W, which is still far sufficient.

Calculation Floor Heating

Unfortunately, there is no documentation available for ~~underfloor heating (FBH)~~ in the kitchen. For this reason, we determine the output of underfloor heating using the room load, as suggested by the German Federal Association for Surface Heating and Cooling (Bundesverband Flächenheizung und Flächenkühlung e.V. (BVF).

This recommendation comes from the BVF guidelines for the approximate hydraulic balancing of existing underfloor heating systems. As a result, we only need to look at Figure 13 in the second step of this series and read off the room load of the kitchen (room no. 4). The room load is 610 W.

Example Calculation with an Online Radiator Calculator

In this sample calculation, I use the online radiator output calculator from the German Heat Pump Association (Bundesverband Wärmepumpe e.V.), which will save you a lot of work. You can use it to easily calculate the radiator output for panel radiators, cast iron radiators, tubular steel radiators and steel radiators. For our towel radiators and underfloor heating, we still need the manual calculation.

In the following steps, I will show you how to calculate the flat panel radiator from anteroom 1 using the online radiator calculator. The following data is given:

Radiator type: Valve radiator PKP 21
Depth: 80 mm
Height: 500 mm
Width: 800 mm
Flow temperature: 75°C
Return temperature: 55 °C
Room temperature: 22 °C

First go to the page of the radiator calculator and select “Translate” via the properties of your browser. In the Chrome browser, for example, click on the three dots in the top right-hand corner, select “Translate” (fig. 3) and then the language.

Figure 3: Translate the Website via your Browser

Then select the correct radiator, as shown in Figure 4. In our case, this is a profiled panel (flat) radiator

Figure 4: Screenshot of the radiator calculator from the German Heat Pump Association – selecting the radiator type

In the next step, enter the data for the radiator, as shown in Figure 5.

Figure 5: Screenshot of the radiator calculator Bundesverband Wärmepumpe e.V. - Calculate radiator output and enter data — Figure 5: Screenshot of the radiator calculator Bundesverband Wärmepumpe e.V. – Calculate radiator output and enter data

The result is 782 W. We have calculated 781.3 W manually in the section“Calculation of panel radiators“. The small deviation is due to rounding. The radiator calculator therefore works really well and can save you a lot of time. For the towel radiator and floor heating, however, you must choose the manual option.

Overview of all Calculated Radiator Outputs

Below you will find the list with the calculated radiator outputs of all radiators in our example building for the system temperatures 75/55/22. I have determined the radiator output once manually (HD) and once with the online calculator (OR). The small deviations are due to rounding. In the following steps, the manually determined values are used for further calculations.

Note: Radiator 3 is a smooth-walled panel radiator.

Room	HK no.	Room load	HK capacity HD (75/55/22)	HK capacity OR (75/55/22)
Anteroom (GF)	1	630 W	781 W	782 W
Toilet (GF)	2	90 W	391 W	391 W
Washroom (GF)	3	130 W	281 W	281 W
Kitchen (GF)	4	610 W	610 W	–
Living room (GF)	5	1830 W	1501 W	1502 W
	6		1501 W	1502 W
Corridor (GF)	7	380 W	433 W	434 W
Bedroom (UF)	8	550 W	1092 W	1092 W
Bathroom (UF)	9	410 W	758 W	–
Office (UF)	10	990 W	819 W	819 W
Guest (UF)	11	670 W	1019 W	1020 W

Table 1: Radiator output of the panel radiators manually, with online calculator and different

Conclusion

It is very interesting to see how the vast majority of radiators in the renovated example building are oversized. I was very surprised by this fact. In the toilet on the ground floor, the oversizing is over 334 %. In the living room, with a system temperature of 75/55/22, it is still 64 % and with an assumed system temperature of 70/50/22, it is still 39 %.

There are two areas with undersized radiators. These are the corridor in the basement and the office on the upper floor. As I assume that the radiator in the basement of the hallway is part of the underfloor heating in the kitchen, the radiator in the hallway should be counted as part of the heating in the kitchen. The hallway should be supplied with sufficient heat via the heat losses from the neighbouring rooms to the hallway. I have described underfloor heating in more detail in the following article: Underfloor heating or underfloor heating.

The radiator output in the office would currently be too low to achieve a room temperature of 22 °C. As the office is not currently used as an office, it would be possible to convert it into a bedroom. A room temperature of 18 °C could then be aimed for. The existing radiator output would be just sufficient with a system temperature of 75/55/18 (924 W) and would only fall short of the room load of 990 W by approx. 6 %. Alternatively, it would be advisable to install a radiator with a higher output.

With the data now obtained, we are able to determine the flow rates of the individual radiators and the default settings for different valve types in the next step.

Below you will find an overview of the “Hydronic Balancing DIY” series:

Overview of the series:

Hydronic Balancing DIY – Example for a detached house
Hydronic Balancing DIY – Step 1: Fundamentals
Hydronic Balancing DIY – Step 2: Heating Load Calculation
Hydronic Balancing DIY – Step 3: Data Recording
Hydronic Balancing DIY – Step 4: Calculate Radiator Output
Hydronic Balancing DIY – Underfloor Heating and Floor heating?
Hydronic Balancing DIY – Step 5: Calculate volumetric flow rate
Hydronic Balancing DIY – Step 6: Presetting the radiator valves
Hydronic Balancing DIY – Step 7: Calculate heating pump

Related articles outside the series:

What is hydronic balancing?
How do Thermostatic Radiator Valves work?
Calculation of old radiators in stock
What does a hydraulic balance cost?

Important: Before you start with the instructions for hydronic balancing, I would like to point out that the procedures described here are based on my personal experience and my personal train of thought. Trying out and implementing the procedures described is entirely at your own risk and responsibility. I do not accept any responsibility. Furthermore, I recommend that you always have the calculated values checked by a specialised company or engineering firm. Because even if the method described here seems simple, calculation errors can always creep in.

I hope that I was able to show you the calculation of the existing radiators in our example building in an understandable way. If you have any questions, suggestions or criticism, please use the comments function.

Best regards! Martin

Further links and sources:
DeltaQ – Heating surface types (Recknagel Sprenger)
Guide for the approximate hydraulic balancing of existing underfloor heating systems
Online radiator calculator from Bundesverband Wärmepumpe e.V.

Cover picture: I created the cover picture with DALL-E from OpenAI.

About Me

Hi, my name is Martin and I’m a passionate engineer in the field of buildings technology. Here you can read who I am and why I write this blog.

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