What are the default font sizes (in pixels) for the html heading tags (<h1>, <h2>, <h3>, etc.)?

I think it is as follows:

h1 is 2 em
h2 is 1.5 em
h3 is 1.3 em
h4 is 1 em
h5 is 0.8 em
h6 is 0.7 em

An em is not the same as a pixel. It is a relative way of looking at sizes. With that said I think most browsers default to 16px (or 1em).

Another way of putting it is:

h1 is   32px   (2em)
h2 is   24px (1.5em)
h3 is 20.8px (1.3em)
h4 is   16px   (1em)
h5 is 12.8px (0.8em)
h6 is 11.2px (0.7em)

For an actual proof, take a look at the html.css (171 - 237) with the default style of Mozilla Firefox:

h1 {
  font-size: 2em;
}

h2 {
  font-size: 1.5em;
}

h3 {
  font-size: 1.17em;
}

h4 {
  font-size: 1.00em;
}

h5 {
  font-size: 0.83em;
}

h6 {
  font-size: 0.67em;
}

The whole css is:

h1 {
  display: block;
  font-size: 2em;
  font-weight: bold;
  margin-block-start: .67em;
  margin-block-end: .67em;
}

h2,
:-moz-any(article, aside, nav, section)
h1 {
  display: block;
  font-size: 1.5em;
  font-weight: bold;
  margin-block-start: .83em;
  margin-block-end: .83em;
}

h3,
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
h1 {
  display: block;
  font-size: 1.17em;
  font-weight: bold;
  margin-block-start: 1em;
  margin-block-end: 1em;
}

h4,
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
h1 {
  display: block;
  font-size: 1.00em;
  font-weight: bold;
  margin-block-start: 1.33em;
  margin-block-end: 1.33em;
}

h5,
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
h1 {
  display: block;
  font-size: 0.83em;
  font-weight: bold;
  margin-block-start: 1.67em;
  margin-block-end: 1.67em;
}

h6,
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
:-moz-any(article, aside, nav, section)
h1 {
  display: block;
  font-size: 0.67em;
  font-weight: bold;
  margin-block-start: 2.33em;
  margin-block-end: 2.33em;
}