(surface-integral-output)=
# Surface Integral Output

*Surface Integral Output computes surface integrals of custom user variables on selected surfaces and can optionally report moving statistics over time.*

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## Available Options

| *Option* | *Description* | *Applicable* |
|----------|---------------|--------------|
| **Output fields** | Custom user variables to integrate over the assigned surfaces | always |
| **Statistics function** | Optional moving statistic applied to the integrated values | always |
| **Moving window size** | Window size for moving statistics (in output data points) | when **Statistics function** is not `None` |
| **Start step** | Step at which to start statistics calculation | when **Statistics function** is not `None` |
| **Assigned surfaces** | Surfaces used for the integral | always |

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## Detailed Descriptions

### Output fields

*The custom user variables to integrate over the selected surfaces.*

- **Required** (at least one field must be selected)
- **Allowed fields:** Custom user variables only
- **Example:** `PressureForce`, `HingeTorqueZ`
>**Note:** Surface Integral Output only accepts custom user variables. Define them in [Variable Settings](../../../05.tools/02.variable-settings.md) (Custom variables tab).

### Statistics function

*Optional moving statistic applied to the integrated values. When set to `None`, raw integral values are reported.*

- **Default:** `None`
- **Options:**
  - `None` - No statistics processing
  - `Mean` - Moving average
  - `Min` - Minimum in the window
  - `Max` - Maximum in the window
  - `Standard deviation` - Sample standard deviation (Bessel's correction)
  - `Deviation` - Range (maximum minus minimum) in the window

### Moving window size

*The number of output data points used in the moving statistics window.*

- **Default:** `10`
- **Minimum value:** `2`
>**Note:** For steady simulations, the solver typically outputs a data point every 10 pseudo steps. For unsteady simulations, it outputs every physical step.

### Start step

*The number of steps to skip before statistics calculation begins.*

- **Default:** `0`
>**Note:** For steady simulations, this value is rounded up to the nearest multiple of 10 (based on output cadence).

### Assigned surfaces

*The surfaces on which the integral is computed.*

- **Required:** Yes (at least one surface must be selected)
- **Supported surface types:**
  - Simulation surfaces (mesh boundaries)
  - Imported sample surfaces
>**Notes:**
> - Import sample surfaces in the Entities browser before selecting them. See [Sample Surfaces](../../../04.entities-browser/10.sample-surfaces.md).
> - Do not mix simulation surfaces and imported sample surfaces in a single Surface Integral Output. Create separate outputs if you need both.

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## Use Cases

Surface Integral Output is useful for:

- Computing hinge torques, forces, or moments defined as custom variables
- Integrating heat flux or other derived quantities over selected surfaces
- Monitoring integrated quantities with moving statistics during transient simulations