Scientific Notation Calculator
Convert numbers to and from scientific notation, and perform arithmetic directly on scientific notation values. Accepts 1.23e5 and 1.23 × 10^5 formats.
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How It Works
Enter any decimal number. The calculator finds the exponent n = floor(log₁₀|x|) and coefficient c = x / 10^n, ensuring 1 ≤ |c| < 10. Both coefficient and exponent display separately alongside the full notation. Very large numbers (like the national debt in dollars) and very small numbers (like atom sizes) convert instantly.
x = c × 10^n where 1 ≤ |c| < 10 | n = floor(log₁₀|x|)0.000456 → 4.56 × 10^(−4) | 299792458 → 2.998 × 10^8Enter in either format: 4.56e-4 or 4.56 × 10^-4. The calculator computes c × 10^n and shows the full decimal form. For very large exponents (e.g. 10^23) the result is too long to display as a full integer — it shows in standard floating-point representation. The original scientific notation also shows alongside.
c × 10^n = c × (10 × 10 × ... × 10) | move decimal n places4.56e-4 → 0.000456 | 6.022e23 → 6.022 × 10^23 (too large for full integer)Enter two numbers in any accepted format. Select ×. Coefficients multiply; exponents add. (3 × 10^8) × (2 × 10^3) = 6 × 10^11. If the product coefficient falls outside [1, 10), the calculator adjusts automatically: (5 × 10^4) × (3 × 10^4) = 15 × 10^8 → normalized to 1.5 × 10^9.
(c₁ × 10^n₁) × (c₂ × 10^n₂) = (c₁ × c₂) × 10^(n₁+n₂)3e8 × 2e3 = 6 × 10^11 | 1.5e5 × 4e2 = 6 × 10^7Division: divide the coefficients and subtract the exponents. (6 × 10^9) ÷ (2 × 10^3) = 3 × 10^6. Enter 6e9 in the first field, ÷, 2e3 in the second — result 3 × 10^6. Normalization happens automatically if the result coefficient falls outside [1, 10).
(c₁ × 10^n₁) ÷ (c₂ × 10^n₂) = (c₁/c₂) × 10^(n₁−n₂)6e9 ÷ 2e3 = 3 × 10^6 | 9e8 ÷ 3e11 = 3 × 10^(−3) = 0.003Addition and subtraction require matching exponents. The calculator converts both numbers to standard form, adds or subtracts, then normalizes the result back to scientific notation. (3 × 10^8) + (5 × 10^7) → 300000000 + 50000000 = 350000000 → 3.5 × 10^8. The result is always properly normalized.
Convert both to standard, add/subtract, then normalize back3e8 + 5e7 = 3.5 × 10^8 | 2.5e6 − 3e5 = 2.2 × 10^6Quick Reference
Common conversions and calculations — verify these in the calculator above.
→ Scientific
0.000456 →
4.56 × 10⁻⁴
→ Scientific
299,792,458 →
2.998 × 10⁸
→ Standard
4.56e-4 →
0.000456
→ Standard
6.022e23 →
6.022 × 10²³
Multiply
3e8 × 2e3
6 × 10¹¹
Divide
6e9 ÷ 2e3
3 × 10⁶
Add
3e8 + 5e7
3.5 × 10⁸
Subtract
2.5e6 − 3e5
2.2 × 10⁶
Tips & Shortcuts
Both input formats work — 1.23e5 and 1.23 × 10^5 are identical. Use whichever you copy from your textbook or spreadsheet without reformatting.
For multiplication and division, remember the quick mental rule: multiply/divide the first digits and add/subtract the exponents. (2 × 10^6) × (3 × 10^4) = 6 × 10^10 in your head.
When the result shows "too large for full integer," copy the scientific notation form — it has all significant figures. The standard decimal would have 20+ digits that obscure the precision.
Use the "Number → Scientific" mode to check how many significant figures your measurement has. The coefficient shows the significant figures; trailing zeros after the decimal all count.
For Avogadro's number (6.022e23) or other constants, use "Scientific → Number" to see what the full decimal would look like — it confirms the extreme size compared to everyday numbers.
Common Mistakes
Entering "1.23 * 10^5" with an asterisk instead of ×
The calculator requires "×" (multiplication sign) not "*" (asterisk) in the 1.23 × 10^5 format. Alternatively, use E-notation: 1.23e5 — no multiplication sign needed and always accepted.
Forgetting that adding scientific notation requires matching exponents manually
In arithmetic mode, the calculator handles exponent matching automatically — just enter both numbers and press Calculate. If doing it by hand, always convert the smaller exponent to match the larger one before adding coefficients.
Confusing coefficient with the full number
In 3.5 × 10^8, the coefficient is 3.5 — not 350000000. The coefficient is always the number between 1 and 10. If your coefficient shows as 35 or 0.35, the notation is not in standard form — use "Number → Scientific" to normalize it.
Using negative coefficient for negative numbers instead of a negative exponent
A negative number in scientific notation is −4.56 × 10^3 (negative coefficient, positive exponent = −4560). A number smaller than 1 uses a positive coefficient with a negative exponent: 4.56 × 10^(−3) = 0.00456. These are very different values.
Expecting "Scientific → Number" to show the full integer for very large exponents
Numbers like 6.022 × 10^23 have 24 digits — larger than standard floating-point can represent exactly. The calculator shows the floating-point approximation. For exact large integers, use the Exponent tab: enter base 10 and exponent 23, then multiply by 6.022 manually.
Frequently Asked Questions
Select "Number → Scientific" mode. Enter any standard number — integer, decimal, or very large/small. Press Convert. The result shows as c × 10^n where 1 ≤ |c| < 10. The coefficient and exponent display separately. Example: 0.000456 → coefficient 4.56, exponent −4, written 4.56 × 10^(−4). Negative exponent means the number is less than 1.
Two formats work identically: E-notation (1.23e5 or 1.23e-4) and standard scientific notation (1.23 × 10^5 or 1.23 × 10^-4). Copy-paste from a spreadsheet, textbook, or physics problem — both are parsed the same way. Standard decimal numbers (12300, 0.00123) work in the "Number → Scientific" direction.
Use arithmetic mode. Enter 3e8 in the first field, select ×, enter 2e3 in the second field, press Calculate. Result: 6 × 10^11. The rule: multiply the coefficients (3 × 2 = 6), add the exponents (8 + 3 = 11). Speed of light × 1000: (3 × 10^8) × (10^3) = 3 × 10^11 m/s × km conversion.
Enter both in arithmetic mode and select + or −. The calculator converts to standard form, adds/subtracts, then converts the result back. Manual method: match exponents first, then add coefficients. (3 × 10^8) + (5 × 10^7) = (3 × 10^8) + (0.5 × 10^8) = 3.5 × 10^8. The calculator handles the exponent matching automatically.
The coefficient (also called significand or mantissa) is the decimal number between 1 and 10: in c × 10^n, the coefficient is c where 1 ≤ |c| < 10. In 6.022 × 10^23, coefficient = 6.022 and exponent = 23. The number of significant figures in the coefficient determines the precision of the measurement. Avogadro's number has 4 significant figures in the coefficient.
E-notation is computer shorthand: 1.23e5 = 1.23 × 10^5 = 123,000. The "E" stands for "exponent of 10." Spreadsheets (Excel, Google Sheets) display large numbers in E-notation automatically. Calculators often show "1.23E+05". Both mean exactly the same thing — this calculator accepts and produces both formats.
Speed of light: 2.998 × 10^8 m/s. Electron charge: 1.602 × 10^(−19) C. Proton mass: 1.673 × 10^(−27) kg. Avogadro's number: 6.022 × 10^23 mol^(−1). Planck's constant: 6.626 × 10^(−34) J·s. Enter any of these in "Scientific → Number" mode to see the full decimal form — though most will display in scientific notation due to their extreme size.
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