箱（はこ）の重（おも）さを測（はか）ってください。

食（た）べたことのない甘（あま）さのクッキーを作（つく）りたい。

何（なに）この汚（きたな）さ！早（はや）く掃除（そうじ）をしてください。

琵琶湖（びわこ）の深（ふか）さって知（し）っている？

日本（にほん）の素晴（すば）らしさを体験（たいけん）したいよ。

この美（うつく）しさは初（はじ）めてです。

彼（かれ）の元気（げんき）さは子供（こども）みたい。

この甘（あま）さは美味（おい）しい。

この景色（けしき）の綺麗（きれい）さは言葉（ことば）では説明（せつめい）できない。

昨日（きのう）食（た）べたラーメンの美味（おい）しさを友達（ともだち）に教（おし）えたい。

この寒（さむ）さだけで死（し）ぬよ。

彼（かれ）がやったことの酷（ひど）さは永遠（えいえん）に忘（わす）れない。

さ and み differences further explained

<div class='writeup-body'>
 さ is a suffix in Japanese that can be attached to the stem form of い-Adjectives and な-Adjectives. When this happens, it transforms the target adjective into a noun that illustrates the 'amount' of that particular adjective. This commonly translates as '-ness' in English (sweetness, tallness, spiciness, etc), but is referred to as degree in Japanese.
 <ul class='writeup-examples--holder'>
 <li class='writeup-example'>
 <div class='writeup-example--japanese'>
 私（わたし）が道（みち）の長（なが）さを測（はか）ります。
 </div>
 <div class='writeup-example--english'>
 I will measure the length of the road. (The road's lengthiness)
 </div>
 </li>
 <li class='writeup-example'>
 <div class='writeup-example--japanese'>
 大人（おとな）になってから家族（かぞく）の大切（たいせつ）さが分（わ）かってきた。
 </div>
 <div class='writeup-example--english'>
 After becoming an adult, I came to understand the importance of family. (Family's importantness)
 </div>
 </li>
 </ul>
 <div class='writeup-funfact'>
 <div class='funfact-header'>Fun Fact</div>
 It is thought that this suffix originally stemmed from the kanji 差（さ） (meaning 'distinction'), and was used for highlighting things that were distinctive features of something. In this way, さ is also sometimes used after the dictionary form of verbs, to highlight a distinct point in time that something happens.
 <ul class='writeup-examples--holder'>
 <li class='writeup-example'>
 <div class='writeup-example--japanese'>学校（がっこう）からの帰（かえ）るさにお金（かね）を拾（ひろ）った。</div>
 <div class='writeup-example--english'>On the way back from school, I picked up some money. (At the 'point' of returning home)</div>
 </li>
 <li class='writeup-example'>
 <div class='writeup-example--japanese'>
 行（い）くさで家（いえ）に忘（わす）れ物（もの）をしたことを思（おも）い出（だ）した。
 </div>
 <div class='writeup-example--english'>
 When I was on my way there, I remembered that I had left something at home. (At the 'point' of going somewhere)
 </div>
 </li>
 </ul>
 However, this use of the suffix is far less common in modern Japanese, and is known as 'poetic language'. It was primarily used during Japan's 'middle ages', which spanned from (around) 1100, until close to the end of the 1500's.
 </div>
</div>

Grammar Info

さ

Converting adjectives to nouns