Is the JAVA html to pdf conversion free?

You can use Cloudmersive Convert API which is free for commercial use like JAVA HTML to PDF up to 1K conversions/month. Here is how you can call it in Java:

// Import classes:
//import com.cloudmersive.client.invoker.ApiClient;
//import com.cloudmersive.client.invoker.ApiException;
//import com.cloudmersive.client.invoker.Configuration;
//import com.cloudmersive.client.invoker.auth.*;
//import com.cloudmersive.client.ConvertDocumentApi;
ApiClient defaultClient = Configuration.getDefaultApiClient();
// Configure API key authorization: Api Key
ApiKeyAuth Api Key = (ApiKeyAuth) defaultClient.getAuthentication("Apikey");
Apikey.setApiKey("YOUR API KEY");
// Uncomment the following line to set a prefix for the API key, e.g. "Token" (defaults to null)
//Apikey.setApiKeyPrefix("Token");
ConvertDocumentApi apiInstance = new ConvertDocumentApi();

File inputFile = new File("/path/to/inputfile"); // File | Input file to perform the operation on.

Boolean includeBackgroundGraphics = true; // Boolean | Optional: Set to true to include background graphics in the PDF, or false to not include. Default is true.

Integer scaleFactor = 56; // Integer | Optional: Set to 100 to scale at 100%, set to 50% to scale down to 50% scale, set to 200% to scale up to 200% scale, etc. Default is 100%. Maximum is 1000%.

try {
    byte[] result = apiInstance.convertDocumentHtmlToPdf(inputFile, includeBackgroundGraphics, scaleFactor);
    System.out.println(result);
} catch (ApiException e) {
    System.err.println("Exception when calling ConvertDocumentApi#convertDocumentHtmlToPdf");
    e.printStackTrace();
}