---
title: Mean Squared Error (MSE)
description: Compute mean squared error (MSE).
canonical: 'https://lightning.ai/docs/torchmetrics/stable/regression/mean_squared_error'
---
# Mean Squared Error (MSE) {#mean-squared-error-mse}

## Module Interface {#module-interface}

### `class torchmetrics.MeanSquaredError(squared=True, num_outputs=1, **kwargs)` {#torchmetrics.MeanSquaredError}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/mse.py#L29-L152)

Compute [mean squared error](https://en.wikipedia.org/wiki/Mean_squared_error) (MSE).

```math
\text{MSE} = \frac{1}{N}\sum_i^N(y_i - \hat{y_i})^2
```

Where $`y`$ is a tensor of target values, and $`\hat{y}`$ is a tensor of predictions.

As input to `forward` and `update` the metric accepts the following input:

*   `preds` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): Predictions from model
    
*   `target` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): Ground truth values
    

As output of `forward` and `compute` the metric returns the following output:

*   `mean_squared_error` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A tensor with the mean squared error
    

Parameters:

*   **squared** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – If True returns MSE value, if False returns RMSE value.
    
*   **num\_outputs** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Number of outputs in multioutput setting
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example::

Single output mse computation:

```python
>>> from torch import tensor
>>> from torchmetrics.regression import MeanSquaredError
>>> target = tensor([2.5, 5.0, 4.0, 8.0])
>>> preds = tensor([3.0, 5.0, 2.5, 7.0])
>>> mean_squared_error = MeanSquaredError()
>>> mean_squared_error(preds, target)
tensor(0.8750)
```

Example::

Multioutput mse computation:

```python
>>> from torch import tensor
>>> from torchmetrics.regression import MeanSquaredError
>>> target = tensor([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])
>>> preds = tensor([[1.0, 2.0, 3.0], [1.0, 2.0, 3.0]])
>>> mean_squared_error = MeanSquaredError(num_outputs=3)
>>> mean_squared_error(preds, target)
tensor([1., 4., 9.])
```

#### `plot(val=None, ax=None)` {#torchmetrics.MeanSquaredError.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/regression/mse.py#L112-L152)

Plot a single or multiple values from the metric.

Parameters:

*   **val** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Sequence`](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> from torch import randn
>>> # Example plotting a single value
>>> from torchmetrics.regression import MeanSquaredError
>>> metric = MeanSquaredError()
>>> metric.update(randn(10,), randn(10,))
>>> fig_, ax_ = metric.plot()
```

[![../../\_images/mean\_squared\_error-1.png](/docs/torchmetrics/1.9.0/static/_images/mean_squared_error-1.png)](/docs/torchmetrics/1.9.0/static/_images/mean_squared_error-1.png)

```python
>>> from torch import randn
>>> # Example plotting multiple values
>>> from torchmetrics.regression import MeanSquaredError
>>> metric = MeanSquaredError()
>>> values = []
>>> for _ in range(10):
...     values.append(metric(randn(10,), randn(10,)))
>>> fig, ax = metric.plot(values)
```

[![../../\_images/mean\_squared\_error-2.png](/docs/torchmetrics/1.9.0/static/_images/mean_squared_error-2.png)](/docs/torchmetrics/1.9.0/static/_images/mean_squared_error-2.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.mean_squared_error(preds, target, squared=True, num_outputs=1)` {#torchmetrics.functional.mean_squared_error}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/regression/mse.py#L61-L82)

Compute mean squared error.

Parameters:

*   **preds** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – estimated labels
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – ground truth labels
    
*   **squared** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – returns RMSE value if set to False
    
*   **num\_outputs** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Number of outputs in multioutput setting
    

Return type:

[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")

Returns:

Tensor with MSE

Example

```python
>>> from torchmetrics.functional.regression import mean_squared_error
>>> x = torch.tensor([0., 1, 2, 3])
>>> y = torch.tensor([0., 1, 2, 2])
>>> mean_squared_error(x, y)
tensor(0.2500)
```

---

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- Parent: [Regression](/docs/torchmetrics/1.9.0/regression.md)