how can i know exactly how fast my animation is going when I hit alt + a?

alright here’s my problem. I’m working on an animation and when I hit alt + a it goes a certain speed. When I render it it goes 3x faster than when I hit alt+a because my computer is kind of slow. Even if i remove the subsurf modifier and hit alt+a I still don’t know if it’s going to go at the same speed when I render it. Is there a way to know when I hit alt+a if it’s going to go at the same speed as when I render it?

I don’t think so, even if you render the stills and playback, it still isn’t always realtime.
What I do is render a playblast of the scene in AVIjpeg format, then lay it back in a video player.

what’s a playblast if you don’t mind me asking? lol

A simple forum search for playblast will tell you, a good definition in this thread

For 2.49b:

“Playblast” is a fairly generic term referring to a “pre-viz” quality rendering of your animation. It’s done by rendering using the OpenGL render button at the far right of the 3D window menu bar. When you hover over this button its tooltip is “Render this window (Ctrl click for anim).” What is rendered is exactly what’s shown in the 3D window, but often cropped depending on the pixel dimensions shown in the Format tab. If you have an Active Camera view in a 3D window it will render that view instead of the the entire window.

The renderings will look like what you see in the UI, no lighting, no AA/OSA, which means it renders very fast. In Blender’s Anim panel is a button labeled PLAY that will playback the latest animated rendering made by Blender – if you render to a movie format like Avi codec, this will allow you to see the action at your chosen playback speed. Alternately you can view the playblast in an external player as long as it can accept the format you specify in the Format tab. Note that you should choose a codec to compress the playblast video, since any player app will tend to work slow with raw .avi files.

Note that in 2.5 the Open GL render seems to be buggy and does odd things, so I wouldn’t recommend using it for any but the roughest pre-viz.

To answer your question:

Is there a way to know when I hit alt+a if it’s going to go at the same speed as when I render it?
When you hit alt+a, you will notice in the upper left corner of the 3D view that Blender shows you your current playback fps, which means frames per second. if that is displaying at the same speed as the FPS framerate setting in your render settings, then you will know that it is playing back at the same speed that it will when rendered.

Only if you enable it in User Prefs.