Decimal Calculator
Welcome to Calcugo's decimal calculator, where we'll walk you through adding, subtracting, multiplying, and dividing decimals, as well as decimal exponents, square roots of a decimal, and logarithms with decimals. Use the Operation drop-down to select any of the seven available operations, enter your values, and hit Calculate for an instant result with a step-by-step formula.
Adding Decimals Calculator
To add two decimals, select Addition (a + b) from the drop-down. The most important rule when adding decimals is keeping track of the decimal point. Both numbers must have the same number of digits after the decimal, so we pad the shorter one with trailing zeros before aligning and adding column by column — just like integer addition. For example, 12.3 + 1.719 becomes 12.300 + 1.719 = 14.019.
Subtracting Decimals Calculator
Select Subtraction (a − b) to subtract one decimal from another. The process mirrors addition: equalise the number of decimal places, then apply standard long subtraction. For example, 5.1 − 2.34 is rewritten as 5.10 − 2.34 = 2.76.
Multiplying Decimals Calculator
Choose Multiplication (a × b) to multiply any two decimals. Multiply as if the numbers were integers, then place the decimal point by counting the total number of decimal places in both factors. For example, 1.2 × 3.45 = 4.14 (1 + 2 = 3 decimal places total, so the result has 3 d.p.).
Dividing Decimals Calculator
Select Division (a ÷ b) to divide one decimal by another. Shift the decimal in the divisor until it becomes a whole number, apply the same shift to the dividend, then divide normally. For example, 1.44 ÷ 0.12 = 144 ÷ 12 = 12.
Decimal Exponents
Choose Exponent (aᵇ) to raise a decimal base to any power. For integer exponents the calculator shows a step-by-step multiplication. For example, 1.5² = 1.5 × 1.5 = 2.25. Fractional exponents represent roots: 8^(1/3) = ∛8 = 2.
(Square) Root of a Decimal
Select Square Root (√a) and enter only the radicand in the a field. The calculator returns √a to full precision. For example, √2.25 = 1.5. Very large or very small results are also shown in scientific notation.
Logarithms with Decimals
Choose Logarithm (log_b(a)) and enter the argument in field a and the base in field b. The result is log_b(a) = ln(a) / ln(b). Common cases: log₁₀(100) = 2; log₂(8) = 3; ln(e) = log_e(e) = 1. Both a and b must be positive, and the base b cannot equal 1.
Using the Decimal Calculator
- Pick an Operation from the drop-down.
- Enter the value for a (and b if required).
- Optionally select a Measurement System — US / Imperial, Metric, or Currency — and then pick a specific unit or currency.
- Press Calculate to see the result, formula, and a step-by-step breakdown.
- Use the Share button to save or share your calculation via a unique link.
Measurement Systems & Currencies
The decimal calculator supports three measurement contexts:
- US / Imperial — in, ft, yd, mi, oz, lb, fl oz, pt, qt, gal, and area/volume variants (in², ft², in³, ft³…)
- Metric — mm, cm, m, km, mg, g, kg, t, mL, L, and area/volume variants
- Currency — USD ($), EUR (€), GBP (£), JPY (¥), CAD, AUD, CHF, CNY, INR (₹), BRL (R$), MXN, KRW (₩), SEK, NOK, DKK, HKD, SGD, PLN (zł), CZK (Kč), RUB (₽), TRY (₺), ZAR, MYR, THB (฿)
FAQs
- Why are trailing zeros important when adding or subtracting decimals?
- They ensure both numbers have the same number of decimal places so the columns align correctly — without them you risk adding or subtracting digits of different positional values.
- Can I raise a negative number to a decimal exponent?
- Negative bases with fractional (non-integer) exponents produce complex numbers and are outside the scope of this calculator. Negative bases with integer exponents work fine.
- What base should I use for a natural logarithm?
- Set b to e ≈ 2.71828. The calculator computes log_b(a) = ln(a)/ln(b), which equals ln(a) when b = e.
- Why does my result appear in scientific notation?
- Very large (≥ 1,000,000,000) or very small (< 0.0001) results are displayed in standard and scientific notation simultaneously for readability.
- How do currencies work in this calculator?
- Selecting a currency only adds the currency symbol as a display prefix — the calculator performs pure arithmetic. Use it to add, subtract, multiply, or divide monetary amounts in any supported currency.