The Rounding Calculator displays all types of number rounding simultaneously.
Supports round, ceil, floor, truncate, banker's rounding, rounding to decimal places (1-4), to tens/hundreds/thousands, and significant figures.
Rounding Calculator
Display all rounding types at once — integer, decimal, tens, significant figures, and more.
Panduan Jenis Pembulatan
Round (Pembulatan Standar)
Bulatkan ke bilangan bulat terdekat. Jika bagian desimal ≥ 0,5 maka dibulatkan ke atas; jika < 0,5 ke bawah. Digunakan sehari-hari untuk harga, nilai rapor, statistik sederhana.
Ceil (Ke Atas / Langit-langit)
Selalu bulatkan ke bilangan bulat terdekat yang ≥ nilai asli. Berguna untuk menghitung kebutuhan minimum: jumlah rak, halaman cetak, anggaran minimum.
Floor (Ke Bawah / Lantai)
Selalu bulatkan ke bilangan bulat terdekat yang ≤ nilai asli. Berguna untuk menghitung kapasitas maksimum: jumlah item per kotak, porsi per kemasan.
Truncate (Potong)
Hapus bagian desimal tanpa pembulatan — selalu menuju nol. Berbeda dari floor untuk bilangan negatif: trunc(−2,9) = −2, sedangkan floor(−2,9) = −3. Digunakan di pemrograman untuk konversi tipe integer.
Angka Penting (Significant Figures)
Mempertahankan sejumlah digit bermakna dari awal bilangan, terlepas dari posisi koma. Contoh: 1.234.567 dibulatkan ke 3 angka penting = 1.230.000. Digunakan di ilmu pengetahuan dan teknik untuk menunjukkan presisi pengukuran.
Banker's Rounding (Round Half to Even)
Saat nilai tepat di tengah (x,5), bulatkan ke bilangan genap terdekat: 2,5 → 2; 3,5 → 4. Standar IEEE 754 dan default Python 3. Meminimalkan bias kumulatif dalam perhitungan keuangan dan statistik skala besar.
Pembulatan ke Kelipatan
Bulatkan ke kelipatan 10, 100, 1.000, dsb. Berguna untuk estimasi anggaran, harga eceran (ribuan rupiah), atau representasi grafik dengan skala besar.
IEEE 754 & Floating-Point
Komputer menyimpan angka desimal dalam format biner, sehingga beberapa nilai (misal 0,1) tidak bisa direpresentasikan persis. Inilah mengapa 0,1 + 0,2 ≠ 0,3 di banyak bahasa pemrograman. Banker's rounding dan penggunaan epsilon (Number.EPSILON) membantu mengurangi galat akumulasi ini.
Calculator information
📋 How to use this calculator
- Enter the original number you want to round (it can be negative or a decimal).
- Choose the rounding method: round (nearest), ceil (up), floor (down), or truncate.
- Set the number of decimal places (0-4), or round to the nearest ten, hundred, or thousand.
- For statistical or accounting data, use banker's rounding (round half to even) to reduce bias.
- Use 'significant figures' mode for scientific reports, following standard significance rules.
- Tip: all rounding results are shown side by side so you can easily compare methods.
🧮 Core Rounding Rules
round(x, n) = sign(x) x floor(|x| x 10^n + 0.5) / 10^n; ceil(x) = ceiling(x); floor(x) = floor(x)
- x = the original number
- n = number of decimal places
- floor() = round-down function
- ceiling() = round-up function
- Banker's: if the digit after is exactly 5, round to the nearest even number
Banker's rounding (IEEE 754) reduces cumulative bias when processing millions of numbers.
💡 Worked example: Rounding 2.675 to 2 decimal places
Given:- x = 2.675
- n = 2 (two decimal places)
Steps:- Round half up: 2.675 x 100 = 267.5; +0.5 = 268; / 100 = 2.68.
- Round half to even (banker's): the third decimal is 5, the preceding digit is 7 (odd), so round to even -> 2.68.
- Floor: 2.67 (drop everything after 2 decimals).
- Ceil: 2.68 (always round up).
- Truncate: 2.67 (same as floor for positive numbers).
Result: Round = 2.68; Floor = 2.67; Ceil = 2.68; Truncate = 2.67; Banker's = 2.68.
❓ Frequently asked questions
What is the difference between round, ceil, and floor?
Round goes to the nearest number based on the next digit. Ceil always rounds up (toward +infinity), while floor always rounds down (toward -infinity). For negative numbers, ceil(-2.3) = -2, while floor(-2.3) = -3.
Why do Excel's rounding results sometimes differ from manual calculation?
Excel's ROUND function defaults to round half up, but some programming languages, such as Python 3, default to banker's rounding in their built-in round() function. In addition, IEEE 754 binary representation means 0.1 + 0.2 is not exactly 0.3, so results can differ by one decimal step.
What are significant figures?
Significant figures are the digits that carry meaningful precision in a measurement. The rules: all non-zero digits are significant, zeros between non-zero digits are significant, and trailing zeros after a decimal point are significant. For example, 0.004520 has 4 significant figures. This convention is standard in science and engineering.
When should you use banker's rounding?
Banker's rounding is well suited to accounting and statistics, where thousands of transactions are rounded and you do not want an upward bias. The IEEE 754 floating-point standard also selects it as the default. For basic education and short reports, round half up is more common because it is easier to explain.
How do you round a price to the nearest thousand?
Divide the value by 1,000, round to an integer using your chosen method (round/floor/ceil), then multiply back by 1,000. Example: $47,350 rounded to the nearest thousand = round(47.35) x 1,000 = $47,000. Retailers often use floor to make prices feel more attractive psychologically.
📚 Sources & references
Last updated: May 11, 2026