Common Log Calculator
Compute the base-10 logarithm of a positive number.
Calculator
Use the Common Log Calculator
Result
—
Formula
log₁₀(x)
Step-by-step
- 1
Enter a positive number
log is defined for x > 0.
- 2
Read the result
The power of 10 that gives x.
Worked example
Example input: n: 1000
Result: 3
Related tools
- Natural Log
Logarithm base e.
Frequently asked questions
What is the common log of 1000?
Exactly 3, because 10³ = 1000. The common log asks the question ten to what power gives this number, and the calculator answers it directly — enter 1000 above and the output is 3 with no rounding. The pattern repeats cleanly: each extra zero in the input adds exactly one to the answer, as with 10, 100, and 1000. Exact powers of ten come back clean, with no rounding noise.
How do I switch between log base 10 and the natural log?
Divide by ln(10) ≈ 2.3026: log₁₀(x) = ln(x) ÷ 2.3026. As a check, ln(100) ≈ 4.6052, and 4.6052 ÷ 2.3026 = 2, which is exactly log₁₀(100).
Why is the log of a small number negative?
Because exponents below zero produce fractions: log₁₀(0.1) = -1 since 10⁻¹ = 0.1, and log₁₀(0.01) = -2. Zero and negative numbers have no real logarithm at all.