Multiplier (Proportion) Calculator
Given X of a quantity in Y total, compute multiplier for other quantities. For recipes, scaling, dosing.
Multiplication factor: proportional scaling
The multiplication factor is the ratio that turns one reference value into another. You find it with factor = A_new / A and apply it with B_new = B · factor. This is really the rule of three (a proportion) written out step by step. Say a recipe uses 350 ml of water for 100 g of flour; scaling up to 250 g gives a factor of 2.5 and 875 ml of water. The factor also reads as a percentage: 1.5 means the value went up 50%, while 0.8 means it dropped 20%. The catch is that proportional scaling only holds when A and B move in a strictly linear way. It breaks down once fixed costs, threshold effects or non-linear physics enter the picture. Multiply a cake recipe by ten, for instance, and the baking time does not multiply by ten.
Applications and context
You will run into this when scaling a recipe, reading engineering drawings and map scales, working out chemistry dilutions (C₁V₁ = C₂V₂), extrapolating a quote or budget, or turning a unit price into a bulk order. In a spreadsheet the same logic shows up as the "rule of three" or "cross multiplication".
FAQ
What's the difference vs percentage change? Percentage change is just factor − 1 written as a percent. A factor of 1.20 is the same as a +20% change.
When does proportional scaling break? Once you hit fixed costs, capacity limits, non-linear physical effects like drying or heating, or economies of scale.
Can the factor be negative? In pure math, sure. In practice both values should carry the same sign. A negative factor flips the direction and rarely lines up with what the real problem is asking.
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Cutting Force by the Kienzle Equation
Computes the main cutting force with the Kienzle equation, F_c = k_c1.1 · b · h^(1 − m_c), where k_c1.1 is the tabulated specific cutting force of the workpiece material for a reference chip section of 1 mm × 1 mm, b is the chip width and h the chip thickness, and m_c is the exponent describing the size effect. That is exactly where it differs from the direct calculation F_c = k_s·b·h: the latter treats specific pressure as a material constant, while Kienzle embeds the experimental fact that thin chips cost far more force per unit area, because the cutting edge radius stops being negligible next to the chip thickness. With k_c1.1 = 1500 N/mm² and m_c = 0.26, a 0.2 mm thick chip works at 2279 N/mm², 52 % above the tabulated value — which is why very low feeds raise the power spent per cubic millimetre removed, and the tool wear with it, instead of saving them — even though the absolute force falls. Since k_c1.1 carries a hidden millimetre raised to m_c, the equation is not dimensionally pure: thickness and width have to be entered in millimetres, and switching units is off by orders of magnitude. Enter the specific force k_c1.1, the exponent m_c, the chip width and the chip thickness.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.