Last updated: September 20, 2026
The idea in one paragraph
A room doesn't jump to a new temperature. It drifts toward the temperature its surroundings and equipment are pushing it to, quickly at first and then more slowly. The calculator models exactly that. It estimates where your room starts, estimates where it is heading, and then works out how far along that path it has travelled.
Step 1: Estimate the starting temperature
Everything begins with the outdoor temperature. From there, the calculator estimates a likely starting indoor temperature using your window setting and room size. With windows open, outdoor air mixes freely with the room, so the starting point sits much closer to the outdoor reading. With windows closed, the room is somewhat insulated and starts nearer a neutral indoor baseline.
Step 2: Find the temperature the room is heading toward
This is called the equilibrium temperature. It is where the room would eventually settle if nothing changed.
- No AC or heater: the room settles near a neutral indoor baseline, which is pulled toward the outdoor temperature.
- AC or heater running: the equilibrium is pulled toward the set temperature you choose. It is pulled only part of the way, because heat keeps leaking in or out through the building. That's why the room typically settles close to the set temperature rather than exactly on it.
- Windows open: conditioned air escapes, so the AC or heater is less effective and the equilibrium sits much closer to the outdoor temperature.
Illustration (not a real output). Suppose it is 40 °C outside, the windows are closed, and the AC is set to 24 °C. The room heads toward a temperature somewhat above 24 °C, because outdoor heat keeps working against the AC. Open the windows and that target moves much closer to 40 °C.
Step 3: Move along the approach curve
The estimator then moves the room from its starting temperature toward its equilibrium temperature using an exponential approach curve. This is the same principle behind Newton's law of cooling. In its general form:
T(t) = Teq + (Tstart − Teq) × e−t/τ
- T(t) is the estimated indoor temperature after running for time t.
- Tstart is the starting temperature from Step 1.
- Teq is the equilibrium temperature from Step 2.
- τ (tau) is a time constant. A small τ means the room responds quickly. A large τ means it responds slowly.
In plain terms, most of the change happens early. After the first hour or two the room is close to its equilibrium, and further gains are small.
How running time is handled
Instead of asking for an exact number of minutes, the calculator asks you to pick a range. Each choice is converted to a representative time:
| You choose | Time used in the model |
|---|---|
| Less than 30 min | 0.25 hours (15 minutes) |
| 30–60 min | 0.75 hours (45 minutes) |
| 1–2 hrs | 1.5 hours |
| 2–4 hrs | 3 hours |
| 4+ hrs | 6 hours |
What each input changes
| Input | Starting point | Equilibrium | Speed |
|---|---|---|---|
| Outdoor temperature | Yes | Yes | No |
| Windows open or closed | Yes | Yes | No |
| AC or heater set temperature | No | Yes | No |
| AC or heater running time | No | No | Sets how far along the curve the room is |
| Fan | No | No | Speeds up the approach. Alone, it has only a small effect. |
| Room size | Yes | No | Smaller rooms respond faster |
A fan doesn't cool or heat air. It circulates it. Together with the AC or heater, it helps the room reach its equilibrium sooner and more evenly. Room size affects how quickly the room changes, not where it ends up.
Range, confidence, and comfort level
Alongside the estimate, the calculator shows a likely range and a confidence level. These describe how much uncertainty the model itself carries. They are not a measurement precision. The comfort level and the gauge (Cold, Comfortable, Hot) simply place the estimated temperature on a common-sense scale.
What the model leaves out
This is a deliberately simple model. It does not account for:
- Insulation quality
- Sun exposure and the direction your windows face
- Humidity
- How many people are in the room
- Building materials and construction
Any of these can move your real room temperature away from the estimate, sometimes by several degrees. That is why the result comes with a range, and why an indoor thermometer will always be more accurate.
Changes to the model
If the method changes in a meaningful way, this page will be updated and the date at the top will change. Spotted something that doesn't add up? Let us know.