# How to estimating the heating cost of an open bathroom window?

I forgot to close the bathroom window in the morning and the heating was on. I'm wondering if it's possible to roughly estimate the costs?

Unfortuantely I have not much physics knowledge. I just need a rough estimate, but searching the internet I did not find a satisfactory answer to my question, but similar questions, so I thought it might be interesting for others too.

The scenario:

The window (60x60cm) was open for 11 hours. Outside temperature approx -10°C. The window is next to the wall mounted heater, the window pane covers the heater when opened. Especially it covers the electric heat cost allocator. During that time the heater thermostat (located near the floor) was on 1 (Defrost), but the heater itself was very hot when I returned. The heater is a wall mounted bathroom heater with an estimated capacity of 960W (EN442) (for more details see page 22 in this brochure) The bathroom door was closed. The bathroom is approx 13m³ large. The energy supplier accounts 6ct/kwh.

My calculation:

I assume the heater was heating all the time at full power, since the thermostat was in the cold air falling down the window, opening the hot water flow to the max.

1) Can I just calculate 11h*0,96w*6ct/kWh = 63,36ct ?

2) I think EN442 defines the heat capacity at a certain temperature (75C/65C/20C, which is water temp in/out/room temp). So is it ok to use 960W for my scenario? Is that the maximum capacity for a heater like that or could it get much higher?

3) I'm not quite sure how the heat cost allocator (sample) calculates costs. I think it measures the difference between the room temperature and the heater. Does it make a huge difference that the window pane (double glass) was in front of it? Could the pane have shielded the allocator a bit from the cold air? Basically is it still accurate under such extreme conditions?

• Your gas and electric company probably can give you help with this. Dec 9, 2017 at 23:53