Calculator
Why Calculators Show Tiny Errors
Updated October 2, 2026
Computers can't store π exactly, so tiny errors leak into trig answers. The maths says sin(180°) is 0. The raw computer value is a number so small it's basically zero—often shown as something like 1.2246e-16.
What you see vs what the machine stores
| You type | Maths says | Raw computer value | Why |
|---|---|---|---|
| sin(180°) | 0 | 1.2246e-16 | π is rounded inside the computer |
| cos(90°) | 0 | 6.1232e-17 | Same reason |
| tan(90°) | undefined | 1.6331e16 | cos(90°) is tiny, so the division explodes |
| 0.1 + 0.2 | 0.3 | 0.30000000000000004 | 0.1 can't be stored exactly in binary |
| 200 × 1.15 | 230 | 229.99999999999997 | 1.15 can't be stored exactly either |
| 171! | too big | Infinity | The limit is about 1.8 × 10^308 |
| sqrt(−4) | not a real number | Error | Real numbers have no negative square roots |
How CalcSolver displays answers
CalcSolver rounds what it shows you to 10 digits, so you'll usually see 0 for sin(180°) and 230 for 200 × 1.15. The raw value can still contain float noise; the display hides it for everyday use.
On the homepage, the “Try it yourself” box shows Raw value next to What CalcSolver shows for the same expression.
Reading e-notation
1.2246e-16 means 1.2246 × 10^−16, which is 0.00000000000000012246.
- 1.5e3 = 1,500
- 4.5e-3 = 0.0045
- 6.02e23 = 602,000,000,000,000,000,000,000
Round once at the end
Rounding early adds up. Keep precision while you work, then round for the final answer. That same advice applies to fractions: don't replace 1/3 with 0.33 mid-calculation (Fractions as decimals and percents).
Practice on the scientific calculator, and review key mistakes in How to use a scientific calculator.